{"id":28995,"date":"2021-05-05T13:00:10","date_gmt":"2021-05-05T13:00:10","guid":{"rendered":"http:\/\/toposuranos.com\/material\/?p=28995"},"modified":"2024-09-22T01:54:47","modified_gmt":"2024-09-22T01:54:47","slug":"%e0%a4%b9%e0%a4%be%e0%a4%87%e0%a4%aa%e0%a4%b0%e0%a4%ac%e0%a5%8b%e0%a4%b2%e0%a4%be-%e0%a4%95%e0%a4%be-%e0%a4%b8%e0%a4%ae%e0%a5%80%e0%a4%95%e0%a4%b0%e0%a4%a3-%e0%a4%94%e0%a4%b0-%e0%a4%87%e0%a4%b8","status":"publish","type":"post","link":"http:\/\/toposuranos.com\/material\/hi\/%e0%a4%b9%e0%a4%be%e0%a4%87%e0%a4%aa%e0%a4%b0%e0%a4%ac%e0%a5%8b%e0%a4%b2%e0%a4%be-%e0%a4%95%e0%a4%be-%e0%a4%b8%e0%a4%ae%e0%a5%80%e0%a4%95%e0%a4%b0%e0%a4%a3-%e0%a4%94%e0%a4%b0-%e0%a4%87%e0%a4%b8\/","title":{"rendered":"\u0939\u093e\u0907\u092a\u0930\u092c\u094b\u0932\u093e \u0915\u093e \u0938\u092e\u0940\u0915\u0930\u0923 \u0914\u0930 \u0907\u0938\u0915\u093e \u0928\u093f\u0930\u0942\u092a\u0923"},"content":{"rendered":"<p><center><\/p>\n<h1>\u0939\u093e\u0907\u092a\u0930\u092c\u094b\u0932\u093e \u0915\u093e \u0938\u092e\u0940\u0915\u0930\u0923 \u0914\u0930 \u0907\u0938\u0915\u093e \u0928\u093f\u0930\u0942\u092a\u0923<\/h1>\n<p><em><strong>\u0938\u093e\u0930\u093e\u0902\u0936:<\/strong><br \/>\n\u0907\u0938 \u0915\u0915\u094d\u0937\u093e \u092e\u0947\u0902 \u0939\u092e \u0939\u093e\u0907\u092a\u0930\u092c\u094b\u0932\u093e \u0915\u0940 \u091c\u094d\u092f\u093e\u092e\u093f\u0924\u0940\u092f \u092a\u0930\u093f\u092d\u093e\u0937\u093e \u0915\u093e \u0905\u0927\u094d\u092f\u092f\u0928 \u0915\u0930\u0947\u0902\u0917\u0947, \u0907\u0938\u0947 \u0905\u0902\u0921\u093e\u0915\u093e\u0930 \u0938\u0947 \u0924\u0941\u0932\u0928\u093e \u0915\u0930\u0947\u0902\u0917\u0947, \u0914\u0930 \u0907\u0938\u0915\u0947 \u0938\u093e\u092e\u093e\u0928\u094d\u092f \u0914\u0930 \u092e\u093e\u0928\u0915 \u0938\u092e\u0940\u0915\u0930\u0923 \u0915\u093e \u0928\u093f\u0930\u0942\u092a\u0923 \u0915\u0930\u0947\u0902\u0917\u0947\u0964<br \/>\n   <\/em><\/p>\n<p>   <strong>\u0938\u0940\u0916\u0928\u0947 \u0915\u0947 \u0932\u0915\u094d\u0937\u094d\u092f:<\/strong><br \/>\n   \u0907\u0938 \u0915\u0915\u094d\u0937\u093e \u0915\u0947 \u0905\u0902\u0924 \u092e\u0947\u0902, \u091b\u093e\u0924\u094d\u0930 \u0938\u0915\u094d\u0937\u092e \u0939\u094b\u0902\u0917\u0947:<\/p>\n<ol style=\"text-align:left;\">\n<li><strong>\u091c\u094d\u092f\u093e\u092e\u093f\u0924\u0940\u092f \u0930\u0942\u092a \u0938\u0947<\/strong> \u0939\u093e\u0907\u092a\u0930\u092c\u094b\u0932\u093e \u0915\u0940 \u092a\u0930\u093f\u092d\u093e\u0937\u093e \u0915\u0930\u0928\u0947 \u092e\u0947\u0902\u0964<\/li>\n<li><strong>\u0928\u093f\u0930\u0942\u092a\u093f\u0924<\/strong> \u0915\u0930\u0928\u0947 \u092e\u0947\u0902 \u0915\u093f \u0939\u093e\u0907\u092a\u0930\u092c\u094b\u0932\u093e \u0915\u0947 \u0938\u093e\u092e\u093e\u0928\u094d\u092f \u0914\u0930 \u092e\u093e\u0928\u0915 \u0938\u092e\u0940\u0915\u0930\u0923 \u0915\u094b \u0909\u0938\u0915\u0940 \u091c\u094d\u092f\u093e\u092e\u093f\u0924\u0940\u092f \u092a\u0930\u093f\u092d\u093e\u0937\u093e \u0938\u0947 \u0915\u0948\u0938\u0947 \u0928\u093f\u0915\u093e\u0932\u093e \u091c\u093e\u0924\u093e \u0939\u0948\u0964<\/li>\n<li><strong>\u092a\u0939\u091a\u093e\u0928\u0928\u0947<\/strong> \u092e\u0947\u0902 \u0915\u093f \u0905\u0902\u0921\u093e\u0915\u093e\u0930 \u0914\u0930 \u0939\u093e\u0907\u092a\u0930\u092c\u094b\u0932\u093e \u0915\u0947 \u092b\u094b\u0915\u0932 \u092c\u093f\u0902\u0926\u0941\u0913\u0902 \u0915\u0947 \u092c\u0940\u091a \u0915\u0940 \u0926\u0942\u0930\u0940 \u092e\u0947\u0902 \u0915\u094d\u092f\u093e \u0905\u0902\u0924\u0930 \u0939\u094b\u0924\u093e \u0939\u0948\u0964<\/li>\n<\/ol>\n<p>   <strong>\u0938\u093e\u092e\u0917\u094d\u0930\u0940 \u0938\u0942\u091a\u0915\u093e\u0902\u0915<\/strong><br \/>\n<a href=\"#1\">\u0939\u093e\u0907\u092a\u0930\u092c\u094b\u0932\u093e \u0915\u0940 \u091c\u094d\u092f\u093e\u092e\u093f\u0924\u0940\u092f \u092a\u0930\u093f\u092d\u093e\u0937\u093e<\/a><br \/>\n<a href=\"#2\">\u0939\u093e\u0907\u092a\u0930\u092c\u094b\u0932\u093e \u0938\u092e\u0940\u0915\u0930\u0923 \u0915\u093e \u0928\u093f\u0930\u0942\u092a\u0923<\/a><br \/>\n<a href=\"#3\">\u0939\u093e\u0907\u092a\u0930\u092c\u094b\u0932\u093e \u0915\u093e \u0938\u093e\u092e\u093e\u0928\u094d\u092f \u0938\u092e\u0940\u0915\u0930\u0923<\/a><br \/>\n<a href=\"#4\">\u0939\u093e\u0907\u092a\u0930\u092c\u094b\u0932\u093e \u0915\u093e \u092e\u093e\u0928\u0915 \u0938\u092e\u0940\u0915\u0930\u0923<\/a>\n   <\/p>\n<p>   <\/center><\/p>\n<p>   <center><iframe class=\"lazyload\" width=\"560\" height=\"315\" data-src=\"https:\/\/www.youtube.com\/embed\/1Aearz-E3bk\" title=\"YouTube video player\" frameborder=\"0\" allow=\"accelerometer; autoplay; clipboard-write; encrypted-media; gyroscope; picture-in-picture\" allowfullscreen=\"allowfullscreen\"><\/iframe><\/center><\/p>\n<p><a name=\"1\"><\/a>   <\/p>\n<h2>\u0939\u093e\u0907\u092a\u0930\u092c\u094b\u0932\u093e \u0915\u0940 \u091c\u094d\u092f\u093e\u092e\u093f\u0924\u0940\u092f \u092a\u0930\u093f\u092d\u093e\u0937\u093e<\/h2>\n<p style=\"text-align: justify;\">\u092a\u0939\u0932\u0947 \u0939\u092e\u0928\u0947 \u0905\u0902\u0921\u093e\u0915\u093e\u0930 \u0914\u0930 \u0935\u0943\u0924\u094d\u0924 \u0915\u0947 \u0938\u092e\u0940\u0915\u0930\u0923 \u0915\u0940 \u0938\u092e\u0940\u0915\u094d\u0937\u093e \u0915\u0940 \u0925\u0940 \u0914\u0930 \u092a\u093e\u092f\u093e \u0915\u093f \u0935\u0947 <span class=\"katex-eq\" data-katex-display=\"false\">ax^2 + bx + cy^2 + dy + e = 0<\/span> \u0915\u0947 \u0930\u0942\u092a \u092e\u0947\u0902 \u0939\u094b\u0924\u0947 \u0939\u0948\u0902, \u091c\u0939\u093e\u0902 <span class=\"katex-eq\" data-katex-display=\"false\">a<\/span> \u0914\u0930 <span class=\"katex-eq\" data-katex-display=\"false\">b<\/span> \u0926\u094b \u0917\u0948\u0930-\u0936\u0942\u0928\u094d\u092f \u092e\u093e\u0928 \u0939\u094b\u0924\u0947 \u0939\u0948\u0902 \u0914\u0930 \u0907\u0928\u0915\u093e \u091a\u093f\u0928\u094d\u0939 \u0938\u092e\u093e\u0928 \u0939\u094b\u0924\u093e \u0939\u0948\u0964 \u0939\u092e\u0928\u0947 \u0915\u0939\u093e \u0925\u093e \u0915\u093f \u092f\u0926\u093f <span class=\"katex-eq\" data-katex-display=\"false\">a<\/span> \u0914\u0930 <span class=\"katex-eq\" data-katex-display=\"false\">b<\/span> \u0915\u0947 \u091a\u093f\u0928\u094d\u0939 \u0935\u093f\u092a\u0930\u0940\u0924 \u0939\u094b\u0924\u0947 \u0939\u0948\u0902, \u0924\u094b \u0905\u0902\u0921\u093e\u0915\u093e\u0930 \u0915\u0947 \u092c\u091c\u093e\u092f \u0939\u092e\u0947\u0902 \u0939\u093e\u0907\u092a\u0930\u092c\u094b\u0932\u093e \u092e\u093f\u0932\u0924\u093e \u0939\u0948\u0964 \u0939\u092e\u0928\u0947 \u0907\u0938\u0915\u0947 \u092c\u093e\u0930\u0947 \u092e\u0947\u0902 \u0935\u093f\u0938\u094d\u0924\u093e\u0930 \u0938\u0947 \u0928\u0939\u0940\u0902 \u092c\u0924\u093e\u092f\u093e, \u0914\u0930 \u0905\u092c \u0939\u092e \u0907\u0938 \u0915\u092e\u0940 \u0915\u094b \u092a\u0942\u0930\u093e \u0915\u0930\u0947\u0902\u0917\u0947\u0964 \u0939\u092e \u091c\u094d\u092f\u093e\u092e\u093f\u0924\u0940\u092f \u0930\u0942\u092a \u0938\u0947 \u0939\u093e\u0907\u092a\u0930\u092c\u094b\u0932\u093e \u0915\u094b \u092a\u0930\u093f\u092d\u093e\u0937\u093f\u0924 \u0915\u0930\u0947\u0902\u0917\u0947 \u0914\u0930 \u0907\u0938\u0938\u0947 \u0939\u093e\u0907\u092a\u0930\u092c\u094b\u0932\u093e \u0915\u093e \u0938\u093e\u092e\u093e\u0928\u094d\u092f \u0914\u0930 \u092e\u093e\u0928\u0915 \u0938\u092e\u0940\u0915\u0930\u0923 \u092a\u094d\u0930\u093e\u092a\u094d\u0924 \u0915\u0930\u0947\u0902\u0917\u0947\u0964<\/p>\n<p style=\"text-align: justify;\"><a href=\"https:\/\/www.youtube.com\/watch?v=1Aearz-E3bk&amp;t=176s\" target=\"_blank\" rel=\"noopener\"><strong>\u0905\u0902\u0921\u093e\u0915\u093e\u0930 \u0915\u0940 \u092a\u0930\u093f\u092d\u093e\u0937\u093e \u0907\u0938 \u092a\u094d\u0930\u0915\u093e\u0930 \u0939\u0948<\/strong><\/a> \u0915\u093f \u092f\u0939 \u0909\u0928 \u0938\u092d\u0940 \u092c\u093f\u0902\u0926\u0941\u0913\u0902 \u0915\u093e \u0938\u092e\u0942\u0939 \u0939\u094b\u0924\u093e \u0939\u0948 \u091c\u093f\u0928\u0915\u0940 \u0926\u0942\u0930\u0940 \u0926\u094b \u0905\u0928\u094d\u092f \u092c\u093f\u0902\u0926\u0941\u0913\u0902, \u091c\u093f\u0928\u094d\u0939\u0947\u0902 \u092b\u094b\u0915\u0938 \u0915\u0939\u093e \u091c\u093e\u0924\u093e \u0939\u0948, \u0938\u0947 \u091c\u094b\u0921\u093c\u0940 \u091c\u093e\u0924\u0940 \u0939\u0948 \u0914\u0930 \u092f\u0939 \u0939\u092e\u0947\u0936\u093e \u090f\u0915 \u0938\u092e\u093e\u0928 \u0939\u094b\u0924\u0940 \u0939\u0948\u0964 \u0907\u0938\u0940 \u092a\u094d\u0930\u0915\u093e\u0930, \u0939\u093e\u0907\u092a\u0930\u092c\u094b\u0932\u093e \u0909\u0928 \u0938\u092d\u0940 \u092c\u093f\u0902\u0926\u0941\u0913\u0902 \u0915\u093e \u0938\u092e\u0942\u0939 \u0939\u094b\u0924\u093e \u0939\u0948 \u091c\u093f\u0928\u0915\u0940 \u092b\u094b\u0915\u0932 \u092c\u093f\u0902\u0926\u0941\u0913\u0902 \u0938\u0947 \u0926\u0942\u0930\u0940 \u0915\u093e \u0905\u0902\u0924\u0930 \u0939\u092e\u0947\u0936\u093e \u090f\u0915 \u0938\u092e\u093e\u0928 \u0930\u0939\u0924\u093e \u0939\u0948\u0964<\/p>\n<p>   <img decoding=\"async\" src=\"data:image\/gif;base64,R0lGODlhAQABAIAAAAAAAP\/\/\/yH5BAEAAAAALAAAAAABAAEAAAIBRAA7\" data-src=\"https:\/\/1.bp.blogspot.com\/-BNQiwaq_OJs\/YJGda6VHOmI\/AAAAAAAAFDo\/edTQHWwLGGQwyGszR7c-7H74a09ASsK2gCLcBGAsYHQ\/s0\/hiperbola%2Bdefinici%25C3%25B3n%2Bgr%25C3%25A1fica.PNG\" alt=\"\u0939\u093e\u0907\u092a\u0930\u092c\u094b\u0932\u093e \u0915\u0940 \u091c\u094d\u092f\u093e\u092e\u093f\u0924\u0940\u092f \u092a\u0930\u093f\u092d\u093e\u0937\u093e\" class=\" aligncenter lazyload\" width=\"493\" height=\"340\" \/><noscript><img decoding=\"async\" src=\"https:\/\/1.bp.blogspot.com\/-BNQiwaq_OJs\/YJGda6VHOmI\/AAAAAAAAFDo\/edTQHWwLGGQwyGszR7c-7H74a09ASsK2gCLcBGAsYHQ\/s0\/hiperbola%2Bdefinici%25C3%25B3n%2Bgr%25C3%25A1fica.PNG\" alt=\"\u0939\u093e\u0907\u092a\u0930\u092c\u094b\u0932\u093e \u0915\u0940 \u091c\u094d\u092f\u093e\u092e\u093f\u0924\u0940\u092f \u092a\u0930\u093f\u092d\u093e\u0937\u093e\" class=\" aligncenter lazyload\" width=\"493\" height=\"340\" \/><\/noscript><\/p>\n<p style=\"text-align: justify;\">\u0905\u0930\u094d\u0925\u093e\u0924, \u092f\u0939 \u0938\u0902\u092c\u0902\u0927 \u092a\u0942\u0930\u093e \u0939\u094b\u0924\u093e \u0939\u0948:<\/p>\n<p style=\"text-align: center;\"><span class=\"katex-eq\" data-katex-display=\"false\">|d(f_1,P) - d(f_2,P)| = 2a<\/span>\n<p style=\"text-align: justify;\">\u091c\u0939\u093e\u0902 <span class=\"katex-eq\" data-katex-display=\"false\">a<\/span> \u090f\u0915 \u0938\u094d\u0925\u093f\u0930 \u0935\u093e\u0938\u094d\u0924\u0935\u093f\u0915 \u0938\u0902\u0916\u094d\u092f\u093e \u0939\u0948\u0964<\/p>\n<p style=\"text-align: justify;\">\u0907\u0938\u0938\u0947 \u0935\u093e\u0938\u094d\u0924\u0935 \u092e\u0947\u0902 \u0926\u094b \u0938\u092e\u0940\u0915\u0930\u0923 \u092a\u094d\u0930\u093e\u092a\u094d\u0924 \u0939\u094b\u0924\u0947 \u0939\u0948\u0902: <span class=\"katex-eq\" data-katex-display=\"false\">d(f_1,P) - d(f_2,P) = 2a<\/span> \u0914\u0930 <span class=\"katex-eq\" data-katex-display=\"false\">d(f_2,P) - d(f_1,P) = 2a<\/span>, \u091c\u093f\u0928\u092e\u0947\u0902 \u0938\u0947 \u092a\u094d\u0930\u0924\u094d\u092f\u0947\u0915 \u0939\u093e\u0907\u092a\u0930\u092c\u094b\u0932\u093e \u0915\u0940 \u090f\u0915 \u0936\u093e\u0916\u093e \u0915\u093e \u092a\u094d\u0930\u0924\u093f\u0928\u093f\u0927\u093f\u0924\u094d\u0935 \u0915\u0930\u0924\u093e \u0939\u0948\u0964<\/p>\n<p><a name=\"2\"><\/a>  <\/p>\n<h2>\u0939\u093e\u0907\u092a\u0930\u092c\u094b\u0932\u093e \u0938\u092e\u0940\u0915\u0930\u0923 \u0915\u093e \u0928\u093f\u0930\u0942\u092a\u0923<\/h2>\n<p style=\"text-align: justify;\"><a href=\"https:\/\/www.youtube.com\/watch?v=1Aearz-E3bk&amp;t=331s\" target=\"_blank\" rel=\"noopener\"><strong>\u091c\u094d\u092f\u093e\u092e\u093f\u0924\u0940\u092f \u092a\u0930\u093f\u092d\u093e\u0937\u093e \u0938\u0947 \u0939\u092e<\/strong><\/a> \u0939\u093e\u0907\u092a\u0930\u092c\u094b\u0932\u093e \u0915\u093e \u092c\u0940\u091c\u0917\u0923\u093f\u0924\u0940\u092f \u0928\u093f\u0930\u0942\u092a\u0923 \u092a\u094d\u0930\u093e\u092a\u094d\u0924 \u0915\u0930 \u0938\u0915\u0924\u0947 \u0939\u0948\u0902\u0964 \u0907\u0938\u0915\u0947 \u0932\u093f\u090f, \u0939\u092e \u0938\u092c\u0938\u0947 \u0938\u0930\u0932 \u0938\u094d\u0925\u093f\u0924\u093f \u0938\u0947 \u0936\u0941\u0930\u0942 \u0915\u0930\u0947\u0902\u0917\u0947 \u0914\u0930 \u0935\u0939\u093e\u0902 \u0938\u0947 \u0938\u093e\u092e\u093e\u0928\u094d\u092f\u0940\u0915\u0930\u0923 \u0915\u0930\u0947\u0902\u0917\u0947\u0964 \u0939\u092e\u093e\u0930\u093e \u0924\u0930\u094d\u0915 \u0915\u0947\u0935\u0932 \u0939\u093e\u0907\u092a\u0930\u092c\u094b\u0932\u093e \u0915\u0940 \u090f\u0915 \u0936\u093e\u0916\u093e \u0915\u0947 \u0932\u093f\u090f \u0939\u094b\u0917\u093e; \u0926\u0942\u0938\u0930\u0940 \u0936\u093e\u0916\u093e \u0915\u093e \u0924\u0930\u094d\u0915 \u0938\u092e\u093e\u0928 \u0939\u094b\u0917\u093e\u0964<\/p>\n<h3>\u0938\u0930\u0932 \u0930\u0942\u092a \u0915\u093e \u0928\u093f\u0930\u0942\u092a\u0923<\/h3>\n<p style=\"text-align: justify;\"><a href=\"https:\/\/www.youtube.com\/watch?v=1Aearz-E3bk&amp;t=356s\" target=\"_blank\" rel=\"noopener\"><strong>\u092e\u093e\u0928 \u0932\u0947\u0902 \u0915\u093f \u0926\u094b \u092b\u094b\u0915\u0932 \u092c\u093f\u0902\u0926\u0941 \u0939\u0948\u0902<\/strong><\/a> <span class=\"katex-eq\" data-katex-display=\"false\">f_1 = (-c,0)<\/span> \u0914\u0930 <span class=\"katex-eq\" data-katex-display=\"false\">f_2 = (c,0).<\/span> \u092c\u093f\u0902\u0926\u0941 <span class=\"katex-eq\" data-katex-display=\"false\">p = (x,y)<\/span> \u0939\u093e\u0907\u092a\u0930\u092c\u094b\u0932\u093e \u092a\u0930 \u0939\u094b\u0917\u093e \u092f\u0926\u093f<\/p>\n<p>   <img decoding=\"async\" src=\"data:image\/gif;base64,R0lGODlhAQABAIAAAAAAAP\/\/\/yH5BAEAAAAALAAAAAABAAEAAAIBRAA7\" data-src=\"https:\/\/1.bp.blogspot.com\/-SMOUgyC1lM4\/YJGg_MIkJTI\/AAAAAAAAFDw\/6JzXOcfZi70lpvTZtbC6y26AvTQzcnWNgCLcBGAsYHQ\/s0\/hiperbola%2Bcentrada%2Ben%2Bel%2Borigen.PNG\" alt=\"\u092e\u0942\u0932 \u092e\u0947\u0902 \u0915\u0947\u0902\u0926\u094d\u0930\u093f\u0924 \u0939\u093e\u0907\u092a\u0930\u092c\u094b\u0932\u093e\" class=\"aligncenter  lazyload\" width=\"342\" height=\"288\" \/><noscript><img decoding=\"async\" src=\"https:\/\/1.bp.blogspot.com\/-SMOUgyC1lM4\/YJGg_MIkJTI\/AAAAAAAAFDw\/6JzXOcfZi70lpvTZtbC6y26AvTQzcnWNgCLcBGAsYHQ\/s0\/hiperbola%2Bcentrada%2Ben%2Bel%2Borigen.PNG\" alt=\"\u092e\u0942\u0932 \u092e\u0947\u0902 \u0915\u0947\u0902\u0926\u094d\u0930\u093f\u0924 \u0939\u093e\u0907\u092a\u0930\u092c\u094b\u0932\u093e\" class=\"aligncenter  lazyload\" width=\"342\" height=\"288\" \/><\/noscript><\/p>\n<p style=\"text-align: center;\"><span class=\"katex-eq\" data-katex-display=\"false\">\\sqrt{(x+c)^2+y^2} - \\sqrt{(x-c)^2+y^2} = 2a<\/span>\n<p>   &nbsp;<\/p>\n<p style=\"text-align: justify;\">\u0914\u0930 \u092f\u0939\u093e\u0902 \u0938\u0947 \u0928\u093f\u092e\u094d\u0928\u0932\u093f\u0916\u093f\u0924 \u0924\u0930\u094d\u0915 \u092a\u094d\u0930\u093e\u092a\u094d\u0924 \u0939\u094b\u0924\u0947 \u0939\u0948\u0902:<\/p>\n<table style=\"text-align: justify;\">\n<tbody>\n<tr>\n<td><span class=\"katex-eq\" data-katex-display=\"false\">\\sqrt{(x+c)^2+y^2} - \\sqrt{(x-c)^2+y^2} = 2a<\/span><\/td>\n<td>; \u0939\u093e\u0907\u092a\u0930\u092c\u094b\u0932\u093e \u0915\u093e \u0938\u092e\u0940\u0915\u0930\u0923<\/td>\n<\/tr>\n<tr><\/tr>\n<tr>\n<td><span class=\"katex-eq\" data-katex-display=\"false\">\\sqrt{x^2 + 2xc + c^2 + y^2} - \\sqrt{x^2 - 2xc + c^2 + y^2} = 2a<\/span><\/td>\n<td>; \u0935\u0930\u094d\u0917\u094b\u0902 \u0915\u093e \u0935\u093f\u0938\u094d\u0924\u093e\u0930<\/td>\n<\/tr>\n<tr><\/tr>\n<tr>\n<td><span class=\"katex-eq\" data-katex-display=\"false\">\\sqrt{x^2 + 2xc + c^2 + y^2} = 2a + \\sqrt{x^2 - 2xc + c^2 + y^2}<\/span><\/td>\n<td>; \u092a\u0926\u094b\u0902 \u0915\u093e \u092a\u0941\u0928\u0930\u094d\u0935\u093f\u0924\u0930\u0923<\/td>\n<\/tr>\n<tr><\/tr>\n<tr>\n<td><span class=\"katex-eq\" data-katex-display=\"false\"> \\color{red}{x^2} + 2xc + \\color{purple}{c^2} + \\color{violet}{y^2} = 4a^2 + 4a\\sqrt{x^2 - 2xc + c^2 + y^2} + \\color{red}{x^2} - 2xc + \\color{purple}{c^2} + \\color{violet}{y^2}<\/span><\/td>\n<td>; \u0926\u094b\u0928\u094b\u0902 \u092a\u0915\u094d\u0937\u094b\u0902 \u0915\u094b \u0935\u0930\u094d\u0917 \u092e\u0947\u0902 \u0932\u0947 \u091c\u093e\u0928\u093e<\/td>\n<\/tr>\n<tr><\/tr>\n<tr>\n<td><span class=\"katex-eq\" data-katex-display=\"false\"> 2xc = 4a^2 + 4a\\sqrt{x^2 - 2xc + c^2 + y^2} - 2xc <\/span><\/td>\n<td>; \u0938\u092e\u093e\u0928 \u092a\u0926\u094b\u0902 \u0915\u093e \u0938\u092e\u093e\u092a\u094d\u0924\u093f<\/td>\n<\/tr>\n<tr><\/tr>\n<tr>\n<td><span class=\"katex-eq\" data-katex-display=\"false\"> 4xc = 4a^2 + 4a\\sqrt{x^2 - 2xc + c^2 + y^2} <\/span><\/td>\n<td>; \u0938\u092e\u093e\u0928 \u092a\u0926\u094b\u0902 \u0915\u093e \u092a\u0941\u0928\u0930\u094d\u0935\u093f\u0924\u0930\u0923<\/td>\n<\/tr>\n<tr><\/tr>\n<tr>\n<td><span class=\"katex-eq\" data-katex-display=\"false\"> xc = a^2 + a\\sqrt{x^2 - 2xc + c^2 + y^2} <\/span><\/td>\n<td>; \u0938\u092e\u093e\u0928 \u092a\u0926\u094b\u0902 \u0915\u093e \u0938\u0930\u0932\u0940\u0915\u0930\u0923<\/td>\n<\/tr>\n<tr><\/tr>\n<tr>\n<td><span class=\"katex-eq\" data-katex-display=\"false\"> xc - a^2 = a\\sqrt{x^2 - 2xc + c^2 + y^2} <\/span><\/td>\n<td>; \u0938\u092e\u093e\u0928 \u092a\u0926\u094b\u0902 \u0915\u093e \u0938\u0930\u0932\u0940\u0915\u0930\u0923<\/td>\n<\/tr>\n<tr><\/tr>\n<tr>\n<td><span class=\"katex-eq\" data-katex-display=\"false\"> x^2c^2 -2xca^2 + a^4 = a^2(x^2 - 2xc + c^2 + y^2) <\/span><\/td>\n<td>; \u0926\u094b\u0928\u094b\u0902 \u092a\u0915\u094d\u0937\u094b\u0902 \u0915\u094b \u0935\u0930\u094d\u0917 \u092e\u0947\u0902 \u0932\u0947\u0928\u093e<\/td>\n<\/tr>\n<tr><\/tr>\n<tr>\n<td><span class=\"katex-eq\" data-katex-display=\"false\"> x^2c^2 \\color{red}{-2xca^2} + a^4 = a^2x^2 \\color{red}{- 2xca^2} + a^2c^2 + a^2y^2 <\/span><\/td>\n<td>; \u0915\u094b\u0937\u094d\u0920\u0915\u094b\u0902 \u0915\u093e \u0909\u092a\u092f\u094b\u0917<\/td>\n<\/tr>\n<tr><\/tr>\n<tr>\n<td><span class=\"katex-eq\" data-katex-display=\"false\"> x^2c^2 + a^4 = a^2x^2 + a^2c^2 + a^2y^2 <\/span><\/td>\n<td>; \u0938\u092e\u093e\u0928 \u092a\u0926\u094b\u0902 \u0915\u093e \u0938\u092e\u093e\u092a\u094d\u0924\u093f<\/td>\n<\/tr>\n<tr><\/tr>\n<tr>\n<td><span class=\"katex-eq\" data-katex-display=\"false\"> x^2(c^2 - a^2) - a^2y^2 = a^2c^2 - a^4 = a^2(c^2 - a^2) <\/span><\/td>\n<td>; \u092a\u0926\u094b\u0902 \u0915\u094b \u092a\u0941\u0928\u0930\u094d\u0917\u0920\u093f\u0924 \u0915\u0930\u0928\u093e<\/td>\n<\/tr>\n<tr><\/tr>\n<tr>\n<td><span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle \\frac{x^2}{a^2} - \\frac{y^2}{c^2 - a^2} = 1 <\/span><\/td>\n<td>; \u092a\u0926\u094b\u0902 \u0915\u093e \u092a\u0941\u0928\u0930\u094d\u0917\u0920\u0928<\/td>\n<\/tr>\n<tr><\/tr>\n<\/tbody>\n<\/table>\n<p style=\"text-align: justify;\">\u0907\u0938 \u0905\u0902\u0924\u093f\u092e \u0905\u092d\u093f\u0935\u094d\u092f\u0915\u094d\u0924\u093f \u0915\u0947 \u0932\u093f\u090f, \u0905\u0902\u0921\u093e\u0915\u093e\u0930 \u0915\u0940 \u0924\u0930\u0939, \u0939\u092e <span class=\"katex-eq\" data-katex-display=\"false\">b^2=c^2-a^2<\/span> \u0932\u0947\u0924\u0947 \u0939\u0948\u0902 \u0914\u0930 \u0939\u093e\u0907\u092a\u0930\u092c\u094b\u0932\u093e \u0915\u0947 \u0938\u092e\u0940\u0915\u0930\u0923 \u092a\u0930 \u092a\u0939\u0941\u0902\u091a\u0924\u0947 \u0939\u0948\u0902:<\/p>\n<p style=\"text-align: center;\"><span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle \\color{blue}{ \\left(\\frac{x}{a}\\right)^2 - \\left(\\frac{y}{b}\\right)^2 = 1 }<\/span>\n<p><a name=\"3\"><\/a>     <\/p>\n<h2>\u0939\u093e\u0907\u092a\u0930\u092c\u094b\u0932\u093e \u0915\u093e \u0938\u093e\u092e\u093e\u0928\u094d\u092f \u0938\u092e\u0940\u0915\u0930\u0923<\/h2>\n<p style=\"text-align: justify;\"><a href=\"https:\/\/www.youtube.com\/watch?v=1Aearz-E3bk&amp;t=801s\" target=\"_blank\" rel=\"noopener\"><strong>\u0938\u093e\u092e\u093e\u0928\u094d\u092f \u0938\u092e\u0940\u0915\u0930\u0923 \u092a\u094d\u0930\u093e\u092a\u094d\u0924 \u0915\u0930\u0928\u0947 \u0915\u0947 \u0932\u093f\u090f<\/strong><\/a> \u0939\u092e\u0947\u0902 \u0915\u0947\u0935\u0932 \u0905\u092c \u0924\u0915 \u092a\u094d\u0930\u093e\u092a\u094d\u0924 \u0915\u093f\u090f \u0917\u090f \u0938\u092e\u0940\u0915\u0930\u0923 \u0915\u094b \u0938\u094d\u0925\u093f\u0924\u093f \u0915\u0947 \u092a\u0930\u093f\u0935\u0930\u094d\u0924\u0928 \u092a\u0930 \u0932\u093e\u0917\u0942 \u0915\u0930\u0928\u093e \u0939\u0948:<\/p>\n<table style=\"text-align: justify;\">\n<tbody>\n<tr>\n<td><span class=\"katex-eq\" data-katex-display=\"false\">x\\longmapsto x-h<\/span><\/td>\n<\/tr>\n<tr>\n<td><span class=\"katex-eq\" data-katex-display=\"false\">y\\longmapsto y-k<\/span><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p style=\"text-align: justify;\">\u0914\u0930 \u0907\u0938\u0915\u0947 \u0938\u093e\u0925 \u0939\u092e \u0938\u094d\u0935\u091a\u093e\u0932\u093f\u0924 \u0930\u0942\u092a \u0938\u0947 \u0915\u0947\u0902\u0926\u094d\u0930 <span class=\"katex-eq\" data-katex-display=\"false\">(h,k)<\/span> \u0915\u0947 \u0938\u093e\u0925 \u0939\u093e\u0907\u092a\u0930\u092c\u094b\u0932\u093e \u0915\u093e \u0938\u093e\u092e\u093e\u0928\u094d\u092f \u0938\u092e\u0940\u0915\u0930\u0923 \u092a\u094d\u0930\u093e\u092a\u094d\u0924 \u0915\u0930\u0924\u0947 \u0939\u0948\u0902:<\/p>\n<p style=\"text-align: center;\"><span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle \\color{blue}{ \\left(\\frac{x-h}{a}\\right)^2 - \\left(\\frac{y-k}{b}\\right)^2 = 1 }<\/span>\n<p><a name=\"4\"><\/a>     <\/p>\n<h2>\u0939\u093e\u0907\u092a\u0930\u092c\u094b\u0932\u093e \u0915\u093e \u092e\u093e\u0928\u0915 \u0938\u092e\u0940\u0915\u0930\u0923<\/h2>\n<p style=\"text-align: justify;\"><a href=\"https:\/\/www.youtube.com\/watch?v=1Aearz-E3bk&amp;t=974s\" target=\"_blank\" rel=\"noopener\"><strong>\u0914\u0930 \u0905\u092c \u092f\u0926\u093f \u0939\u092e \u0938\u093e\u092e\u093e\u0928\u094d\u092f \u0938\u092e\u0940\u0915\u0930\u0923 \u0932\u0947\u0924\u0947 \u0939\u0948\u0902<\/strong><\/a> \u0914\u0930 \u0907\u0938\u0947 \u0935\u093f\u0938\u094d\u0924\u093e\u0930 \u0915\u0930\u0924\u0947 \u0939\u0948\u0902, \u0924\u094b \u0939\u092e \u092e\u093e\u0928\u0915 \u0905\u092d\u093f\u0935\u094d\u092f\u0915\u094d\u0924\u093f \u0924\u0915 \u092a\u0939\u0941\u0902\u091a\u0924\u0947 \u0939\u0948\u0902:<\/p>\n<table style=\"text-align: justify;\">\n<tbody>\n<tr>\n<td><span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle \\left(\\frac{x-h}{a}\\right)^2 - \\left(\\frac{y-k}{b}\\right)^2 = 1<\/span><\/td>\n<td>; \u0939\u093e\u0907\u092a\u0930\u092c\u094b\u0932\u093e \u0915\u093e \u0938\u093e\u092e\u093e\u0928\u094d\u092f \u0938\u092e\u0940\u0915\u0930\u0923<\/td>\n<\/tr>\n<tr>\n<td><span class=\"katex-eq\" data-katex-display=\"false\">b^2 (x^2 - 2xh + h^2) - a^2(y^2-2ky + y^2) = a^2b^2<\/span><\/td>\n<td>; \u0935\u0930\u094d\u0917\u094b\u0902 \u0915\u094b \u0939\u0932 \u0915\u0930\u0928\u093e \u0914\u0930 <span class=\"katex-eq\" data-katex-display=\"false\">a^2b^2<\/span> \u0938\u0947 \u0938\u092c \u0915\u0941\u091b \u0917\u0941\u0923\u093e \u0915\u0930\u0928\u093e<\/td>\n<\/tr>\n<tr>\n<td><span class=\"katex-eq\" data-katex-display=\"false\"> b^2 x^2 - 2hb^2x + h^2b^2 - a^2 y^2+ 2k a^2 y - a^2 k^2 = a^2b^2<\/span><\/td>\n<td>; \u0915\u094b\u0937\u094d\u0920\u0915\u094b\u0902 \u0915\u094b \u0939\u0932 \u0915\u0930\u0928\u093e<\/td>\n<\/tr>\n<tr>\n<td><span class=\"katex-eq\" data-katex-display=\"false\"> b^2 x^2 - (2hb^2) x - a^2 y^2+ (2k a^2) y - (a^2b^2 + a^2 k^2 - h^2b^2) = 0 <\/span><\/td>\n<td>; \u0938\u092e\u093e\u0928 \u092a\u0926\u094b\u0902 \u0915\u093e \u0938\u092e\u0942\u0939<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p style=\"text-align: justify;\">\u092f\u0939 \u0905\u0902\u0924\u093f\u092e \u0905\u092d\u093f\u0935\u094d\u092f\u0915\u094d\u0924\u093f <span class=\"katex-eq\" data-katex-display=\"false\">Ax^2+Bx + Cy^2 + Dy + E = 0,<\/span> \u0915\u0947 \u0930\u0942\u092a \u092e\u0947\u0902 \u0939\u0948, \u091c\u0939\u093e\u0902 <span class=\"katex-eq\" data-katex-display=\"false\">A<\/span> \u0914\u0930 <span class=\"katex-eq\" data-katex-display=\"false\">C<\/span> \u0939\u092e\u0947\u0936\u093e \u0917\u0948\u0930-\u0936\u0942\u0928\u094d\u092f \u0939\u094b\u0924\u0947 \u0939\u0948\u0902 \u0914\u0930 \u0909\u0928\u0915\u0947 \u091a\u093f\u0928\u094d\u0939 \u0935\u093f\u092a\u0930\u0940\u0924 \u0939\u094b\u0924\u0947 \u0939\u0948\u0902, \u091c\u0948\u0938\u093e \u0915\u093f \u0939\u092e\u0928\u0947 \u0905\u0902\u0921\u093e\u0915\u093e\u0930 \u0915\u093e \u0905\u0927\u094d\u092f\u092f\u0928 \u0915\u0930\u0924\u0947 \u0938\u092e\u092f \u0915\u0939\u093e \u0925\u093e\u0964<\/p>\n","protected":false},"excerpt":{"rendered":"<p>\u0939\u093e\u0907\u092a\u0930\u092c\u094b\u0932\u093e \u0915\u093e \u0938\u092e\u0940\u0915\u0930\u0923 \u0914\u0930 \u0907\u0938\u0915\u093e \u0928\u093f\u0930\u0942\u092a\u0923 \u0938\u093e\u0930\u093e\u0902\u0936: \u0907\u0938 \u0915\u0915\u094d\u0937\u093e \u092e\u0947\u0902 \u0939\u092e \u0939\u093e\u0907\u092a\u0930\u092c\u094b\u0932\u093e \u0915\u0940 \u091c\u094d\u092f\u093e\u092e\u093f\u0924\u0940\u092f \u092a\u0930\u093f\u092d\u093e\u0937\u093e \u0915\u093e \u0905\u0927\u094d\u092f\u092f\u0928 \u0915\u0930\u0947\u0902\u0917\u0947, \u0907\u0938\u0947 \u0905\u0902\u0921\u093e\u0915\u093e\u0930 \u0938\u0947 \u0924\u0941\u0932\u0928\u093e \u0915\u0930\u0947\u0902\u0917\u0947, \u0914\u0930 \u0907\u0938\u0915\u0947 \u0938\u093e\u092e\u093e\u0928\u094d\u092f \u0914\u0930 \u092e\u093e\u0928\u0915 \u0938\u092e\u0940\u0915\u0930\u0923 \u0915\u093e \u0928\u093f\u0930\u0942\u092a\u0923 \u0915\u0930\u0947\u0902\u0917\u0947\u0964 \u0938\u0940\u0916\u0928\u0947 \u0915\u0947 \u0932\u0915\u094d\u0937\u094d\u092f: \u0907\u0938 \u0915\u0915\u094d\u0937\u093e \u0915\u0947 \u0905\u0902\u0924 \u092e\u0947\u0902, \u091b\u093e\u0924\u094d\u0930 \u0938\u0915\u094d\u0937\u092e \u0939\u094b\u0902\u0917\u0947: \u091c\u094d\u092f\u093e\u092e\u093f\u0924\u0940\u092f \u0930\u0942\u092a \u0938\u0947 \u0939\u093e\u0907\u092a\u0930\u092c\u094b\u0932\u093e \u0915\u0940 \u092a\u0930\u093f\u092d\u093e\u0937\u093e \u0915\u0930\u0928\u0947 \u092e\u0947\u0902\u0964 \u0928\u093f\u0930\u0942\u092a\u093f\u0924 \u0915\u0930\u0928\u0947 \u092e\u0947\u0902 \u0915\u093f [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":28988,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"iawp_total_views":1,"footnotes":""},"categories":[577,593],"tags":[],"class_list":["post-28995","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-577","category-593"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v26.7 - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>\u0939\u093e\u0907\u092a\u0930\u092c\u094b\u0932\u093e \u0915\u093e \u0938\u092e\u0940\u0915\u0930\u0923 \u0914\u0930 \u0907\u0938\u0915\u093e \u0928\u093f\u0930\u0942\u092a\u0923 - toposuranos.com\/material<\/title>\n<meta name=\"description\" content=\"\u0939\u093e\u0907\u092a\u0930\u092c\u094b\u0932\u093e \u0915\u0947 \u092c\u093e\u0930\u0947 \u092e\u0947\u0902 \u0938\u092c \u0915\u0941\u091b \u091c\u093e\u0928\u0947\u0902: \u091c\u094d\u092f\u093e\u092e\u093f\u0924\u0940\u092f \u092a\u0930\u093f\u092d\u093e\u0937\u093e, \u0907\u0938\u0915\u0947 \u0938\u093e\u092e\u093e\u0928\u094d\u092f \u0914\u0930 \u092e\u093e\u0928\u0915 \u0938\u092e\u0940\u0915\u0930\u0923 \u0915\u093e \u0928\u093f\u0930\u0942\u092a\u0923, \u0907\u0938\u0947 \u0905\u0902\u0921\u093e\u0915\u093e\u0930 \u0938\u0947 \u0915\u0948\u0938\u0947 \u0905\u0932\u0917 \u0915\u093f\u092f\u093e \u091c\u093e\u0924\u093e \u0939\u0948, \u0914\u0930 \u091a\u0930\u0923 \u0926\u0930 \u091a\u0930\u0923 \u0938\u092e\u0940\u0915\u0930\u0923 \u0915\u0948\u0938\u0947 \u0939\u0932 \u0915\u093f\u092f\u093e \u091c\u093e\u090f\u0964 \u0917\u0923\u093f\u0924 \u0914\u0930 \u091c\u094d\u092f\u093e\u092e\u093f\u0924\u093f \u0915\u0947 \u0936\u094c\u0915\u0940\u0928\u094b\u0902 \u0914\u0930 \u091b\u093e\u0924\u094d\u0930\u094b\u0902 \u0915\u0947 \u0932\u093f\u090f \u0909\u092a\u092f\u0941\u0915\u094d\u0924\u0964\" \/>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"http:\/\/toposuranos.com\/material\/hi\/\u0939\u093e\u0907\u092a\u0930\u092c\u094b\u0932\u093e-\u0915\u093e-\u0938\u092e\u0940\u0915\u0930\u0923-\u0914\u0930-\u0907\u0938\/\" \/>\n<meta property=\"og:locale\" content=\"es_ES\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"\u0939\u093e\u0907\u092a\u0930\u092c\u094b\u0932\u093e \u0915\u093e \u0938\u092e\u0940\u0915\u0930\u0923 \u0914\u0930 \u0907\u0938\u0915\u093e \u0928\u093f\u0930\u0942\u092a\u0923\" \/>\n<meta property=\"og:description\" content=\"\u0939\u093e\u0907\u092a\u0930\u092c\u094b\u0932\u093e \u0915\u0947 \u092c\u093e\u0930\u0947 \u092e\u0947\u0902 \u0938\u092c \u0915\u0941\u091b \u091c\u093e\u0928\u0947\u0902: \u091c\u094d\u092f\u093e\u092e\u093f\u0924\u0940\u092f \u092a\u0930\u093f\u092d\u093e\u0937\u093e, \u0907\u0938\u0915\u0947 \u0938\u093e\u092e\u093e\u0928\u094d\u092f \u0914\u0930 \u092e\u093e\u0928\u0915 \u0938\u092e\u0940\u0915\u0930\u0923 \u0915\u093e \u0928\u093f\u0930\u0942\u092a\u0923, \u0907\u0938\u0947 \u0905\u0902\u0921\u093e\u0915\u093e\u0930 \u0938\u0947 \u0915\u0948\u0938\u0947 \u0905\u0932\u0917 \u0915\u093f\u092f\u093e \u091c\u093e\u0924\u093e \u0939\u0948, \u0914\u0930 \u091a\u0930\u0923 \u0926\u0930 \u091a\u0930\u0923 \u0938\u092e\u0940\u0915\u0930\u0923 \u0915\u0948\u0938\u0947 \u0939\u0932 \u0915\u093f\u092f\u093e \u091c\u093e\u090f\u0964 \u0917\u0923\u093f\u0924 \u0914\u0930 \u091c\u094d\u092f\u093e\u092e\u093f\u0924\u093f \u0915\u0947 \u0936\u094c\u0915\u0940\u0928\u094b\u0902 \u0914\u0930 \u091b\u093e\u0924\u094d\u0930\u094b\u0902 \u0915\u0947 \u0932\u093f\u090f \u0909\u092a\u092f\u0941\u0915\u094d\u0924\u0964\" \/>\n<meta property=\"og:url\" content=\"http:\/\/toposuranos.com\/material\/hi\/\u0939\u093e\u0907\u092a\u0930\u092c\u094b\u0932\u093e-\u0915\u093e-\u0938\u092e\u0940\u0915\u0930\u0923-\u0914\u0930-\u0907\u0938\/\" \/>\n<meta property=\"og:site_name\" content=\"toposuranos.com\/material\" \/>\n<meta property=\"article:publisher\" content=\"https:\/\/www.facebook.com\/groups\/toposuranos\" \/>\n<meta property=\"article:published_time\" content=\"2021-05-05T13:00:10+00:00\" \/>\n<meta property=\"article:modified_time\" content=\"2024-09-22T01:54:47+00:00\" \/>\n<meta property=\"og:image\" content=\"http:\/\/toposuranos.com\/material\/wp-content\/uploads\/2024\/09\/hiperbola-centrada-en-el-origen.png\" \/>\n<meta name=\"author\" content=\"giorgio.reveco\" \/>\n<meta name=\"twitter:card\" content=\"summary_large_image\" \/>\n<meta name=\"twitter:title\" content=\"\u0939\u093e\u0907\u092a\u0930\u092c\u094b\u0932\u093e \u0915\u093e \u0938\u092e\u0940\u0915\u0930\u0923 \u0914\u0930 \u0907\u0938\u0915\u093e \u0928\u093f\u0930\u0942\u092a\u0923\" \/>\n<meta name=\"twitter:description\" content=\"\u0939\u093e\u0907\u092a\u0930\u092c\u094b\u0932\u093e \u0915\u0947 \u092c\u093e\u0930\u0947 \u092e\u0947\u0902 \u0938\u092c \u0915\u0941\u091b \u091c\u093e\u0928\u0947\u0902: \u091c\u094d\u092f\u093e\u092e\u093f\u0924\u0940\u092f \u092a\u0930\u093f\u092d\u093e\u0937\u093e, \u0907\u0938\u0915\u0947 \u0938\u093e\u092e\u093e\u0928\u094d\u092f \u0914\u0930 \u092e\u093e\u0928\u0915 \u0938\u092e\u0940\u0915\u0930\u0923 \u0915\u093e \u0928\u093f\u0930\u0942\u092a\u0923, \u0907\u0938\u0947 \u0905\u0902\u0921\u093e\u0915\u093e\u0930 \u0938\u0947 \u0915\u0948\u0938\u0947 \u0905\u0932\u0917 \u0915\u093f\u092f\u093e \u091c\u093e\u0924\u093e \u0939\u0948, \u0914\u0930 \u091a\u0930\u0923 \u0926\u0930 \u091a\u0930\u0923 \u0938\u092e\u0940\u0915\u0930\u0923 \u0915\u0948\u0938\u0947 \u0939\u0932 \u0915\u093f\u092f\u093e \u091c\u093e\u090f\u0964 \u0917\u0923\u093f\u0924 \u0914\u0930 \u091c\u094d\u092f\u093e\u092e\u093f\u0924\u093f \u0915\u0947 \u0936\u094c\u0915\u0940\u0928\u094b\u0902 \u0914\u0930 \u091b\u093e\u0924\u094d\u0930\u094b\u0902 \u0915\u0947 \u0932\u093f\u090f \u0909\u092a\u092f\u0941\u0915\u094d\u0924\u0964\" \/>\n<meta name=\"twitter:image\" content=\"http:\/\/toposuranos.com\/material\/wp-content\/uploads\/2024\/09\/hiperbola-centrada-en-el-origen.png\" \/>\n<meta name=\"twitter:creator\" content=\"@topuranos\" \/>\n<meta name=\"twitter:site\" content=\"@topuranos\" \/>\n<meta name=\"twitter:label1\" content=\"Escrito por\" \/>\n\t<meta name=\"twitter:data1\" content=\"giorgio.reveco\" \/>\n\t<meta name=\"twitter:label2\" content=\"Tiempo de lectura\" \/>\n\t<meta name=\"twitter:data2\" content=\"5 minutos\" \/>\n<script type=\"application\/ld+json\" class=\"yoast-schema-graph\">{\"@context\":\"https:\/\/schema.org\",\"@graph\":[{\"@type\":\"Article\",\"@id\":\"http:\/\/toposuranos.com\/material\/hi\/%e0%a4%b9%e0%a4%be%e0%a4%87%e0%a4%aa%e0%a4%b0%e0%a4%ac%e0%a5%8b%e0%a4%b2%e0%a4%be-%e0%a4%95%e0%a4%be-%e0%a4%b8%e0%a4%ae%e0%a5%80%e0%a4%95%e0%a4%b0%e0%a4%a3-%e0%a4%94%e0%a4%b0-%e0%a4%87%e0%a4%b8\/#article\",\"isPartOf\":{\"@id\":\"http:\/\/toposuranos.com\/material\/hi\/%e0%a4%b9%e0%a4%be%e0%a4%87%e0%a4%aa%e0%a4%b0%e0%a4%ac%e0%a5%8b%e0%a4%b2%e0%a4%be-%e0%a4%95%e0%a4%be-%e0%a4%b8%e0%a4%ae%e0%a5%80%e0%a4%95%e0%a4%b0%e0%a4%a3-%e0%a4%94%e0%a4%b0-%e0%a4%87%e0%a4%b8\/\"},\"author\":{\"name\":\"giorgio.reveco\",\"@id\":\"http:\/\/toposuranos.com\/material\/#\/schema\/person\/e15164361c3f9a2a02cf6c234cf7fdc1\"},\"headline\":\"\u0939\u093e\u0907\u092a\u0930\u092c\u094b\u0932\u093e \u0915\u093e \u0938\u092e\u0940\u0915\u0930\u0923 \u0914\u0930 \u0907\u0938\u0915\u093e \u0928\u093f\u0930\u0942\u092a\u0923\",\"datePublished\":\"2021-05-05T13:00:10+00:00\",\"dateModified\":\"2024-09-22T01:54:47+00:00\",\"mainEntityOfPage\":{\"@id\":\"http:\/\/toposuranos.com\/material\/hi\/%e0%a4%b9%e0%a4%be%e0%a4%87%e0%a4%aa%e0%a4%b0%e0%a4%ac%e0%a5%8b%e0%a4%b2%e0%a4%be-%e0%a4%95%e0%a4%be-%e0%a4%b8%e0%a4%ae%e0%a5%80%e0%a4%95%e0%a4%b0%e0%a4%a3-%e0%a4%94%e0%a4%b0-%e0%a4%87%e0%a4%b8\/\"},\"wordCount\":407,\"commentCount\":0,\"publisher\":{\"@id\":\"http:\/\/toposuranos.com\/material\/#organization\"},\"image\":{\"@id\":\"http:\/\/toposuranos.com\/material\/hi\/%e0%a4%b9%e0%a4%be%e0%a4%87%e0%a4%aa%e0%a4%b0%e0%a4%ac%e0%a5%8b%e0%a4%b2%e0%a4%be-%e0%a4%95%e0%a4%be-%e0%a4%b8%e0%a4%ae%e0%a5%80%e0%a4%95%e0%a4%b0%e0%a4%a3-%e0%a4%94%e0%a4%b0-%e0%a4%87%e0%a4%b8\/#primaryimage\"},\"thumbnailUrl\":\"http:\/\/toposuranos.com\/material\/wp-content\/uploads\/2024\/09\/hiperbola-centrada-en-el-origen.png\",\"articleSection\":[\"\u0917\u0923\u093f\u0924\",\"\u092c\u0940\u091c\u0917\u0923\u093f\u0924 \u0914\u0930 \u0930\u0947\u0916\u093e\u0917\u0923\u093f\u0924\"],\"inLanguage\":\"es\",\"potentialAction\":[{\"@type\":\"CommentAction\",\"name\":\"Comment\",\"target\":[\"http:\/\/toposuranos.com\/material\/hi\/%e0%a4%b9%e0%a4%be%e0%a4%87%e0%a4%aa%e0%a4%b0%e0%a4%ac%e0%a5%8b%e0%a4%b2%e0%a4%be-%e0%a4%95%e0%a4%be-%e0%a4%b8%e0%a4%ae%e0%a5%80%e0%a4%95%e0%a4%b0%e0%a4%a3-%e0%a4%94%e0%a4%b0-%e0%a4%87%e0%a4%b8\/#respond\"]}]},{\"@type\":\"WebPage\",\"@id\":\"http:\/\/toposuranos.com\/material\/hi\/%e0%a4%b9%e0%a4%be%e0%a4%87%e0%a4%aa%e0%a4%b0%e0%a4%ac%e0%a5%8b%e0%a4%b2%e0%a4%be-%e0%a4%95%e0%a4%be-%e0%a4%b8%e0%a4%ae%e0%a5%80%e0%a4%95%e0%a4%b0%e0%a4%a3-%e0%a4%94%e0%a4%b0-%e0%a4%87%e0%a4%b8\/\",\"url\":\"http:\/\/toposuranos.com\/material\/hi\/%e0%a4%b9%e0%a4%be%e0%a4%87%e0%a4%aa%e0%a4%b0%e0%a4%ac%e0%a5%8b%e0%a4%b2%e0%a4%be-%e0%a4%95%e0%a4%be-%e0%a4%b8%e0%a4%ae%e0%a5%80%e0%a4%95%e0%a4%b0%e0%a4%a3-%e0%a4%94%e0%a4%b0-%e0%a4%87%e0%a4%b8\/\",\"name\":\"\u0939\u093e\u0907\u092a\u0930\u092c\u094b\u0932\u093e \u0915\u093e \u0938\u092e\u0940\u0915\u0930\u0923 \u0914\u0930 \u0907\u0938\u0915\u093e \u0928\u093f\u0930\u0942\u092a\u0923 - toposuranos.com\/material\",\"isPartOf\":{\"@id\":\"http:\/\/toposuranos.com\/material\/#website\"},\"primaryImageOfPage\":{\"@id\":\"http:\/\/toposuranos.com\/material\/hi\/%e0%a4%b9%e0%a4%be%e0%a4%87%e0%a4%aa%e0%a4%b0%e0%a4%ac%e0%a5%8b%e0%a4%b2%e0%a4%be-%e0%a4%95%e0%a4%be-%e0%a4%b8%e0%a4%ae%e0%a5%80%e0%a4%95%e0%a4%b0%e0%a4%a3-%e0%a4%94%e0%a4%b0-%e0%a4%87%e0%a4%b8\/#primaryimage\"},\"image\":{\"@id\":\"http:\/\/toposuranos.com\/material\/hi\/%e0%a4%b9%e0%a4%be%e0%a4%87%e0%a4%aa%e0%a4%b0%e0%a4%ac%e0%a5%8b%e0%a4%b2%e0%a4%be-%e0%a4%95%e0%a4%be-%e0%a4%b8%e0%a4%ae%e0%a5%80%e0%a4%95%e0%a4%b0%e0%a4%a3-%e0%a4%94%e0%a4%b0-%e0%a4%87%e0%a4%b8\/#primaryimage\"},\"thumbnailUrl\":\"http:\/\/toposuranos.com\/material\/wp-content\/uploads\/2024\/09\/hiperbola-centrada-en-el-origen.png\",\"datePublished\":\"2021-05-05T13:00:10+00:00\",\"dateModified\":\"2024-09-22T01:54:47+00:00\",\"description\":\"\u0939\u093e\u0907\u092a\u0930\u092c\u094b\u0932\u093e \u0915\u0947 \u092c\u093e\u0930\u0947 \u092e\u0947\u0902 \u0938\u092c \u0915\u0941\u091b \u091c\u093e\u0928\u0947\u0902: \u091c\u094d\u092f\u093e\u092e\u093f\u0924\u0940\u092f \u092a\u0930\u093f\u092d\u093e\u0937\u093e, \u0907\u0938\u0915\u0947 \u0938\u093e\u092e\u093e\u0928\u094d\u092f \u0914\u0930 \u092e\u093e\u0928\u0915 \u0938\u092e\u0940\u0915\u0930\u0923 \u0915\u093e \u0928\u093f\u0930\u0942\u092a\u0923, \u0907\u0938\u0947 \u0905\u0902\u0921\u093e\u0915\u093e\u0930 \u0938\u0947 \u0915\u0948\u0938\u0947 \u0905\u0932\u0917 \u0915\u093f\u092f\u093e \u091c\u093e\u0924\u093e \u0939\u0948, \u0914\u0930 \u091a\u0930\u0923 \u0926\u0930 \u091a\u0930\u0923 \u0938\u092e\u0940\u0915\u0930\u0923 \u0915\u0948\u0938\u0947 \u0939\u0932 \u0915\u093f\u092f\u093e \u091c\u093e\u090f\u0964 \u0917\u0923\u093f\u0924 \u0914\u0930 \u091c\u094d\u092f\u093e\u092e\u093f\u0924\u093f \u0915\u0947 \u0936\u094c\u0915\u0940\u0928\u094b\u0902 \u0914\u0930 \u091b\u093e\u0924\u094d\u0930\u094b\u0902 \u0915\u0947 \u0932\u093f\u090f \u0909\u092a\u092f\u0941\u0915\u094d\u0924\u0964\",\"breadcrumb\":{\"@id\":\"http:\/\/toposuranos.com\/material\/hi\/%e0%a4%b9%e0%a4%be%e0%a4%87%e0%a4%aa%e0%a4%b0%e0%a4%ac%e0%a5%8b%e0%a4%b2%e0%a4%be-%e0%a4%95%e0%a4%be-%e0%a4%b8%e0%a4%ae%e0%a5%80%e0%a4%95%e0%a4%b0%e0%a4%a3-%e0%a4%94%e0%a4%b0-%e0%a4%87%e0%a4%b8\/#breadcrumb\"},\"inLanguage\":\"es\",\"potentialAction\":[{\"@type\":\"ReadAction\",\"target\":[\"http:\/\/toposuranos.com\/material\/hi\/%e0%a4%b9%e0%a4%be%e0%a4%87%e0%a4%aa%e0%a4%b0%e0%a4%ac%e0%a5%8b%e0%a4%b2%e0%a4%be-%e0%a4%95%e0%a4%be-%e0%a4%b8%e0%a4%ae%e0%a5%80%e0%a4%95%e0%a4%b0%e0%a4%a3-%e0%a4%94%e0%a4%b0-%e0%a4%87%e0%a4%b8\/\"]}]},{\"@type\":\"ImageObject\",\"inLanguage\":\"es\",\"@id\":\"http:\/\/toposuranos.com\/material\/hi\/%e0%a4%b9%e0%a4%be%e0%a4%87%e0%a4%aa%e0%a4%b0%e0%a4%ac%e0%a5%8b%e0%a4%b2%e0%a4%be-%e0%a4%95%e0%a4%be-%e0%a4%b8%e0%a4%ae%e0%a5%80%e0%a4%95%e0%a4%b0%e0%a4%a3-%e0%a4%94%e0%a4%b0-%e0%a4%87%e0%a4%b8\/#primaryimage\",\"url\":\"http:\/\/toposuranos.com\/material\/wp-content\/uploads\/2024\/09\/hiperbola-centrada-en-el-origen.png\",\"contentUrl\":\"http:\/\/toposuranos.com\/material\/wp-content\/uploads\/2024\/09\/hiperbola-centrada-en-el-origen.png\",\"width\":484,\"height\":408},{\"@type\":\"BreadcrumbList\",\"@id\":\"http:\/\/toposuranos.com\/material\/hi\/%e0%a4%b9%e0%a4%be%e0%a4%87%e0%a4%aa%e0%a4%b0%e0%a4%ac%e0%a5%8b%e0%a4%b2%e0%a4%be-%e0%a4%95%e0%a4%be-%e0%a4%b8%e0%a4%ae%e0%a5%80%e0%a4%95%e0%a4%b0%e0%a4%a3-%e0%a4%94%e0%a4%b0-%e0%a4%87%e0%a4%b8\/#breadcrumb\",\"itemListElement\":[{\"@type\":\"ListItem\",\"position\":1,\"name\":\"Portada\",\"item\":\"https:\/\/toposuranos.com\/material\/es\/cursos-de-matematica-y-fisica\/\"},{\"@type\":\"ListItem\",\"position\":2,\"name\":\"\u0939\u093e\u0907\u092a\u0930\u092c\u094b\u0932\u093e \u0915\u093e \u0938\u092e\u0940\u0915\u0930\u0923 \u0914\u0930 \u0907\u0938\u0915\u093e \u0928\u093f\u0930\u0942\u092a\u0923\"}]},{\"@type\":\"WebSite\",\"@id\":\"http:\/\/toposuranos.com\/material\/#website\",\"url\":\"http:\/\/toposuranos.com\/material\/\",\"name\":\"toposuranos.com\/material\",\"description\":\"\",\"publisher\":{\"@id\":\"http:\/\/toposuranos.com\/material\/#organization\"},\"potentialAction\":[{\"@type\":\"SearchAction\",\"target\":{\"@type\":\"EntryPoint\",\"urlTemplate\":\"http:\/\/toposuranos.com\/material\/?s={search_term_string}\"},\"query-input\":{\"@type\":\"PropertyValueSpecification\",\"valueRequired\":true,\"valueName\":\"search_term_string\"}}],\"inLanguage\":\"es\"},{\"@type\":\"Organization\",\"@id\":\"http:\/\/toposuranos.com\/material\/#organization\",\"name\":\"toposuranos.com\/material\",\"url\":\"http:\/\/toposuranos.com\/material\/\",\"logo\":{\"@type\":\"ImageObject\",\"inLanguage\":\"es\",\"@id\":\"http:\/\/toposuranos.com\/material\/#\/schema\/logo\/image\/\",\"url\":\"http:\/\/toposuranos.com\/material\/wp-content\/uploads\/2023\/10\/logo.png\",\"contentUrl\":\"http:\/\/toposuranos.com\/material\/wp-content\/uploads\/2023\/10\/logo.png\",\"width\":2400,\"height\":2059,\"caption\":\"toposuranos.com\/material\"},\"image\":{\"@id\":\"http:\/\/toposuranos.com\/material\/#\/schema\/logo\/image\/\"},\"sameAs\":[\"https:\/\/www.facebook.com\/groups\/toposuranos\",\"https:\/\/x.com\/topuranos\",\"https:\/\/www.youtube.com\/channel\/UC16yDm12cPcrwsE0fAM7X1g\",\"https:\/\/www.linkedin.com\/company\/69429190\"]},{\"@type\":\"Person\",\"@id\":\"http:\/\/toposuranos.com\/material\/#\/schema\/person\/e15164361c3f9a2a02cf6c234cf7fdc1\",\"name\":\"giorgio.reveco\",\"image\":{\"@type\":\"ImageObject\",\"inLanguage\":\"es\",\"@id\":\"http:\/\/toposuranos.com\/material\/#\/schema\/person\/image\/\",\"url\":\"http:\/\/toposuranos.com\/material\/wp-content\/uploads\/2023\/10\/1694478625378-96x96.jpeg\",\"contentUrl\":\"http:\/\/toposuranos.com\/material\/wp-content\/uploads\/2023\/10\/1694478625378-96x96.jpeg\",\"caption\":\"giorgio.reveco\"},\"description\":\"Soy Licenciado en F\u00edsica, Magister en Ingenier\u00eda Industrial y Docente Universitario. Me dedico a desmitificar la f\u00edsica y las matem\u00e1ticas. Mi objetivo es hacer que estos campos sean f\u00e1cilmente comprensibles para todos, proporcionando las herramientas para explorar no solo el mundo que nos rodea, sino tambi\u00e9n las profundidades de nuestra propia existencia y el orden natural que nos conecta con el cosmos.\",\"sameAs\":[\"http:\/\/toposuranos.com\/material\"],\"url\":\"http:\/\/toposuranos.com\/material\/author\/giorgio-reveco\/\"}]}<\/script>\n<!-- \/ Yoast SEO plugin. -->","yoast_head_json":{"title":"\u0939\u093e\u0907\u092a\u0930\u092c\u094b\u0932\u093e \u0915\u093e \u0938\u092e\u0940\u0915\u0930\u0923 \u0914\u0930 \u0907\u0938\u0915\u093e \u0928\u093f\u0930\u0942\u092a\u0923 - toposuranos.com\/material","description":"\u0939\u093e\u0907\u092a\u0930\u092c\u094b\u0932\u093e \u0915\u0947 \u092c\u093e\u0930\u0947 \u092e\u0947\u0902 \u0938\u092c \u0915\u0941\u091b \u091c\u093e\u0928\u0947\u0902: \u091c\u094d\u092f\u093e\u092e\u093f\u0924\u0940\u092f \u092a\u0930\u093f\u092d\u093e\u0937\u093e, \u0907\u0938\u0915\u0947 \u0938\u093e\u092e\u093e\u0928\u094d\u092f \u0914\u0930 \u092e\u093e\u0928\u0915 \u0938\u092e\u0940\u0915\u0930\u0923 \u0915\u093e \u0928\u093f\u0930\u0942\u092a\u0923, \u0907\u0938\u0947 \u0905\u0902\u0921\u093e\u0915\u093e\u0930 \u0938\u0947 \u0915\u0948\u0938\u0947 \u0905\u0932\u0917 \u0915\u093f\u092f\u093e \u091c\u093e\u0924\u093e \u0939\u0948, \u0914\u0930 \u091a\u0930\u0923 \u0926\u0930 \u091a\u0930\u0923 \u0938\u092e\u0940\u0915\u0930\u0923 \u0915\u0948\u0938\u0947 \u0939\u0932 \u0915\u093f\u092f\u093e \u091c\u093e\u090f\u0964 \u0917\u0923\u093f\u0924 \u0914\u0930 \u091c\u094d\u092f\u093e\u092e\u093f\u0924\u093f \u0915\u0947 \u0936\u094c\u0915\u0940\u0928\u094b\u0902 \u0914\u0930 \u091b\u093e\u0924\u094d\u0930\u094b\u0902 \u0915\u0947 \u0932\u093f\u090f \u0909\u092a\u092f\u0941\u0915\u094d\u0924\u0964","robots":{"index":"index","follow":"follow","max-snippet":"max-snippet:-1","max-image-preview":"max-image-preview:large","max-video-preview":"max-video-preview:-1"},"canonical":"http:\/\/toposuranos.com\/material\/hi\/\u0939\u093e\u0907\u092a\u0930\u092c\u094b\u0932\u093e-\u0915\u093e-\u0938\u092e\u0940\u0915\u0930\u0923-\u0914\u0930-\u0907\u0938\/","og_locale":"es_ES","og_type":"article","og_title":"\u0939\u093e\u0907\u092a\u0930\u092c\u094b\u0932\u093e \u0915\u093e \u0938\u092e\u0940\u0915\u0930\u0923 \u0914\u0930 \u0907\u0938\u0915\u093e \u0928\u093f\u0930\u0942\u092a\u0923","og_description":"\u0939\u093e\u0907\u092a\u0930\u092c\u094b\u0932\u093e \u0915\u0947 \u092c\u093e\u0930\u0947 \u092e\u0947\u0902 \u0938\u092c \u0915\u0941\u091b \u091c\u093e\u0928\u0947\u0902: \u091c\u094d\u092f\u093e\u092e\u093f\u0924\u0940\u092f \u092a\u0930\u093f\u092d\u093e\u0937\u093e, \u0907\u0938\u0915\u0947 \u0938\u093e\u092e\u093e\u0928\u094d\u092f \u0914\u0930 \u092e\u093e\u0928\u0915 \u0938\u092e\u0940\u0915\u0930\u0923 \u0915\u093e \u0928\u093f\u0930\u0942\u092a\u0923, \u0907\u0938\u0947 \u0905\u0902\u0921\u093e\u0915\u093e\u0930 \u0938\u0947 \u0915\u0948\u0938\u0947 \u0905\u0932\u0917 \u0915\u093f\u092f\u093e \u091c\u093e\u0924\u093e \u0939\u0948, \u0914\u0930 \u091a\u0930\u0923 \u0926\u0930 \u091a\u0930\u0923 \u0938\u092e\u0940\u0915\u0930\u0923 \u0915\u0948\u0938\u0947 \u0939\u0932 \u0915\u093f\u092f\u093e \u091c\u093e\u090f\u0964 \u0917\u0923\u093f\u0924 \u0914\u0930 \u091c\u094d\u092f\u093e\u092e\u093f\u0924\u093f \u0915\u0947 \u0936\u094c\u0915\u0940\u0928\u094b\u0902 \u0914\u0930 \u091b\u093e\u0924\u094d\u0930\u094b\u0902 \u0915\u0947 \u0932\u093f\u090f \u0909\u092a\u092f\u0941\u0915\u094d\u0924\u0964","og_url":"http:\/\/toposuranos.com\/material\/hi\/\u0939\u093e\u0907\u092a\u0930\u092c\u094b\u0932\u093e-\u0915\u093e-\u0938\u092e\u0940\u0915\u0930\u0923-\u0914\u0930-\u0907\u0938\/","og_site_name":"toposuranos.com\/material","article_publisher":"https:\/\/www.facebook.com\/groups\/toposuranos","article_published_time":"2021-05-05T13:00:10+00:00","article_modified_time":"2024-09-22T01:54:47+00:00","og_image":[{"url":"http:\/\/toposuranos.com\/material\/wp-content\/uploads\/2024\/09\/hiperbola-centrada-en-el-origen.png","type":"","width":"","height":""}],"author":"giorgio.reveco","twitter_card":"summary_large_image","twitter_title":"\u0939\u093e\u0907\u092a\u0930\u092c\u094b\u0932\u093e \u0915\u093e \u0938\u092e\u0940\u0915\u0930\u0923 \u0914\u0930 \u0907\u0938\u0915\u093e \u0928\u093f\u0930\u0942\u092a\u0923","twitter_description":"\u0939\u093e\u0907\u092a\u0930\u092c\u094b\u0932\u093e \u0915\u0947 \u092c\u093e\u0930\u0947 \u092e\u0947\u0902 \u0938\u092c \u0915\u0941\u091b \u091c\u093e\u0928\u0947\u0902: \u091c\u094d\u092f\u093e\u092e\u093f\u0924\u0940\u092f \u092a\u0930\u093f\u092d\u093e\u0937\u093e, \u0907\u0938\u0915\u0947 \u0938\u093e\u092e\u093e\u0928\u094d\u092f \u0914\u0930 \u092e\u093e\u0928\u0915 \u0938\u092e\u0940\u0915\u0930\u0923 \u0915\u093e \u0928\u093f\u0930\u0942\u092a\u0923, \u0907\u0938\u0947 \u0905\u0902\u0921\u093e\u0915\u093e\u0930 \u0938\u0947 \u0915\u0948\u0938\u0947 \u0905\u0932\u0917 \u0915\u093f\u092f\u093e \u091c\u093e\u0924\u093e \u0939\u0948, \u0914\u0930 \u091a\u0930\u0923 \u0926\u0930 \u091a\u0930\u0923 \u0938\u092e\u0940\u0915\u0930\u0923 \u0915\u0948\u0938\u0947 \u0939\u0932 \u0915\u093f\u092f\u093e \u091c\u093e\u090f\u0964 \u0917\u0923\u093f\u0924 \u0914\u0930 \u091c\u094d\u092f\u093e\u092e\u093f\u0924\u093f \u0915\u0947 \u0936\u094c\u0915\u0940\u0928\u094b\u0902 \u0914\u0930 \u091b\u093e\u0924\u094d\u0930\u094b\u0902 \u0915\u0947 \u0932\u093f\u090f \u0909\u092a\u092f\u0941\u0915\u094d\u0924\u0964","twitter_image":"http:\/\/toposuranos.com\/material\/wp-content\/uploads\/2024\/09\/hiperbola-centrada-en-el-origen.png","twitter_creator":"@topuranos","twitter_site":"@topuranos","twitter_misc":{"Escrito por":"giorgio.reveco","Tiempo de lectura":"5 minutos"},"schema":{"@context":"https:\/\/schema.org","@graph":[{"@type":"Article","@id":"http:\/\/toposuranos.com\/material\/hi\/%e0%a4%b9%e0%a4%be%e0%a4%87%e0%a4%aa%e0%a4%b0%e0%a4%ac%e0%a5%8b%e0%a4%b2%e0%a4%be-%e0%a4%95%e0%a4%be-%e0%a4%b8%e0%a4%ae%e0%a5%80%e0%a4%95%e0%a4%b0%e0%a4%a3-%e0%a4%94%e0%a4%b0-%e0%a4%87%e0%a4%b8\/#article","isPartOf":{"@id":"http:\/\/toposuranos.com\/material\/hi\/%e0%a4%b9%e0%a4%be%e0%a4%87%e0%a4%aa%e0%a4%b0%e0%a4%ac%e0%a5%8b%e0%a4%b2%e0%a4%be-%e0%a4%95%e0%a4%be-%e0%a4%b8%e0%a4%ae%e0%a5%80%e0%a4%95%e0%a4%b0%e0%a4%a3-%e0%a4%94%e0%a4%b0-%e0%a4%87%e0%a4%b8\/"},"author":{"name":"giorgio.reveco","@id":"http:\/\/toposuranos.com\/material\/#\/schema\/person\/e15164361c3f9a2a02cf6c234cf7fdc1"},"headline":"\u0939\u093e\u0907\u092a\u0930\u092c\u094b\u0932\u093e \u0915\u093e \u0938\u092e\u0940\u0915\u0930\u0923 \u0914\u0930 \u0907\u0938\u0915\u093e \u0928\u093f\u0930\u0942\u092a\u0923","datePublished":"2021-05-05T13:00:10+00:00","dateModified":"2024-09-22T01:54:47+00:00","mainEntityOfPage":{"@id":"http:\/\/toposuranos.com\/material\/hi\/%e0%a4%b9%e0%a4%be%e0%a4%87%e0%a4%aa%e0%a4%b0%e0%a4%ac%e0%a5%8b%e0%a4%b2%e0%a4%be-%e0%a4%95%e0%a4%be-%e0%a4%b8%e0%a4%ae%e0%a5%80%e0%a4%95%e0%a4%b0%e0%a4%a3-%e0%a4%94%e0%a4%b0-%e0%a4%87%e0%a4%b8\/"},"wordCount":407,"commentCount":0,"publisher":{"@id":"http:\/\/toposuranos.com\/material\/#organization"},"image":{"@id":"http:\/\/toposuranos.com\/material\/hi\/%e0%a4%b9%e0%a4%be%e0%a4%87%e0%a4%aa%e0%a4%b0%e0%a4%ac%e0%a5%8b%e0%a4%b2%e0%a4%be-%e0%a4%95%e0%a4%be-%e0%a4%b8%e0%a4%ae%e0%a5%80%e0%a4%95%e0%a4%b0%e0%a4%a3-%e0%a4%94%e0%a4%b0-%e0%a4%87%e0%a4%b8\/#primaryimage"},"thumbnailUrl":"http:\/\/toposuranos.com\/material\/wp-content\/uploads\/2024\/09\/hiperbola-centrada-en-el-origen.png","articleSection":["\u0917\u0923\u093f\u0924","\u092c\u0940\u091c\u0917\u0923\u093f\u0924 \u0914\u0930 \u0930\u0947\u0916\u093e\u0917\u0923\u093f\u0924"],"inLanguage":"es","potentialAction":[{"@type":"CommentAction","name":"Comment","target":["http:\/\/toposuranos.com\/material\/hi\/%e0%a4%b9%e0%a4%be%e0%a4%87%e0%a4%aa%e0%a4%b0%e0%a4%ac%e0%a5%8b%e0%a4%b2%e0%a4%be-%e0%a4%95%e0%a4%be-%e0%a4%b8%e0%a4%ae%e0%a5%80%e0%a4%95%e0%a4%b0%e0%a4%a3-%e0%a4%94%e0%a4%b0-%e0%a4%87%e0%a4%b8\/#respond"]}]},{"@type":"WebPage","@id":"http:\/\/toposuranos.com\/material\/hi\/%e0%a4%b9%e0%a4%be%e0%a4%87%e0%a4%aa%e0%a4%b0%e0%a4%ac%e0%a5%8b%e0%a4%b2%e0%a4%be-%e0%a4%95%e0%a4%be-%e0%a4%b8%e0%a4%ae%e0%a5%80%e0%a4%95%e0%a4%b0%e0%a4%a3-%e0%a4%94%e0%a4%b0-%e0%a4%87%e0%a4%b8\/","url":"http:\/\/toposuranos.com\/material\/hi\/%e0%a4%b9%e0%a4%be%e0%a4%87%e0%a4%aa%e0%a4%b0%e0%a4%ac%e0%a5%8b%e0%a4%b2%e0%a4%be-%e0%a4%95%e0%a4%be-%e0%a4%b8%e0%a4%ae%e0%a5%80%e0%a4%95%e0%a4%b0%e0%a4%a3-%e0%a4%94%e0%a4%b0-%e0%a4%87%e0%a4%b8\/","name":"\u0939\u093e\u0907\u092a\u0930\u092c\u094b\u0932\u093e \u0915\u093e \u0938\u092e\u0940\u0915\u0930\u0923 \u0914\u0930 \u0907\u0938\u0915\u093e \u0928\u093f\u0930\u0942\u092a\u0923 - toposuranos.com\/material","isPartOf":{"@id":"http:\/\/toposuranos.com\/material\/#website"},"primaryImageOfPage":{"@id":"http:\/\/toposuranos.com\/material\/hi\/%e0%a4%b9%e0%a4%be%e0%a4%87%e0%a4%aa%e0%a4%b0%e0%a4%ac%e0%a5%8b%e0%a4%b2%e0%a4%be-%e0%a4%95%e0%a4%be-%e0%a4%b8%e0%a4%ae%e0%a5%80%e0%a4%95%e0%a4%b0%e0%a4%a3-%e0%a4%94%e0%a4%b0-%e0%a4%87%e0%a4%b8\/#primaryimage"},"image":{"@id":"http:\/\/toposuranos.com\/material\/hi\/%e0%a4%b9%e0%a4%be%e0%a4%87%e0%a4%aa%e0%a4%b0%e0%a4%ac%e0%a5%8b%e0%a4%b2%e0%a4%be-%e0%a4%95%e0%a4%be-%e0%a4%b8%e0%a4%ae%e0%a5%80%e0%a4%95%e0%a4%b0%e0%a4%a3-%e0%a4%94%e0%a4%b0-%e0%a4%87%e0%a4%b8\/#primaryimage"},"thumbnailUrl":"http:\/\/toposuranos.com\/material\/wp-content\/uploads\/2024\/09\/hiperbola-centrada-en-el-origen.png","datePublished":"2021-05-05T13:00:10+00:00","dateModified":"2024-09-22T01:54:47+00:00","description":"\u0939\u093e\u0907\u092a\u0930\u092c\u094b\u0932\u093e \u0915\u0947 \u092c\u093e\u0930\u0947 \u092e\u0947\u0902 \u0938\u092c \u0915\u0941\u091b \u091c\u093e\u0928\u0947\u0902: \u091c\u094d\u092f\u093e\u092e\u093f\u0924\u0940\u092f \u092a\u0930\u093f\u092d\u093e\u0937\u093e, \u0907\u0938\u0915\u0947 \u0938\u093e\u092e\u093e\u0928\u094d\u092f \u0914\u0930 \u092e\u093e\u0928\u0915 \u0938\u092e\u0940\u0915\u0930\u0923 \u0915\u093e \u0928\u093f\u0930\u0942\u092a\u0923, \u0907\u0938\u0947 \u0905\u0902\u0921\u093e\u0915\u093e\u0930 \u0938\u0947 \u0915\u0948\u0938\u0947 \u0905\u0932\u0917 \u0915\u093f\u092f\u093e \u091c\u093e\u0924\u093e \u0939\u0948, \u0914\u0930 \u091a\u0930\u0923 \u0926\u0930 \u091a\u0930\u0923 \u0938\u092e\u0940\u0915\u0930\u0923 \u0915\u0948\u0938\u0947 \u0939\u0932 \u0915\u093f\u092f\u093e \u091c\u093e\u090f\u0964 \u0917\u0923\u093f\u0924 \u0914\u0930 \u091c\u094d\u092f\u093e\u092e\u093f\u0924\u093f \u0915\u0947 \u0936\u094c\u0915\u0940\u0928\u094b\u0902 \u0914\u0930 \u091b\u093e\u0924\u094d\u0930\u094b\u0902 \u0915\u0947 \u0932\u093f\u090f \u0909\u092a\u092f\u0941\u0915\u094d\u0924\u0964","breadcrumb":{"@id":"http:\/\/toposuranos.com\/material\/hi\/%e0%a4%b9%e0%a4%be%e0%a4%87%e0%a4%aa%e0%a4%b0%e0%a4%ac%e0%a5%8b%e0%a4%b2%e0%a4%be-%e0%a4%95%e0%a4%be-%e0%a4%b8%e0%a4%ae%e0%a5%80%e0%a4%95%e0%a4%b0%e0%a4%a3-%e0%a4%94%e0%a4%b0-%e0%a4%87%e0%a4%b8\/#breadcrumb"},"inLanguage":"es","potentialAction":[{"@type":"ReadAction","target":["http:\/\/toposuranos.com\/material\/hi\/%e0%a4%b9%e0%a4%be%e0%a4%87%e0%a4%aa%e0%a4%b0%e0%a4%ac%e0%a5%8b%e0%a4%b2%e0%a4%be-%e0%a4%95%e0%a4%be-%e0%a4%b8%e0%a4%ae%e0%a5%80%e0%a4%95%e0%a4%b0%e0%a4%a3-%e0%a4%94%e0%a4%b0-%e0%a4%87%e0%a4%b8\/"]}]},{"@type":"ImageObject","inLanguage":"es","@id":"http:\/\/toposuranos.com\/material\/hi\/%e0%a4%b9%e0%a4%be%e0%a4%87%e0%a4%aa%e0%a4%b0%e0%a4%ac%e0%a5%8b%e0%a4%b2%e0%a4%be-%e0%a4%95%e0%a4%be-%e0%a4%b8%e0%a4%ae%e0%a5%80%e0%a4%95%e0%a4%b0%e0%a4%a3-%e0%a4%94%e0%a4%b0-%e0%a4%87%e0%a4%b8\/#primaryimage","url":"http:\/\/toposuranos.com\/material\/wp-content\/uploads\/2024\/09\/hiperbola-centrada-en-el-origen.png","contentUrl":"http:\/\/toposuranos.com\/material\/wp-content\/uploads\/2024\/09\/hiperbola-centrada-en-el-origen.png","width":484,"height":408},{"@type":"BreadcrumbList","@id":"http:\/\/toposuranos.com\/material\/hi\/%e0%a4%b9%e0%a4%be%e0%a4%87%e0%a4%aa%e0%a4%b0%e0%a4%ac%e0%a5%8b%e0%a4%b2%e0%a4%be-%e0%a4%95%e0%a4%be-%e0%a4%b8%e0%a4%ae%e0%a5%80%e0%a4%95%e0%a4%b0%e0%a4%a3-%e0%a4%94%e0%a4%b0-%e0%a4%87%e0%a4%b8\/#breadcrumb","itemListElement":[{"@type":"ListItem","position":1,"name":"Portada","item":"https:\/\/toposuranos.com\/material\/es\/cursos-de-matematica-y-fisica\/"},{"@type":"ListItem","position":2,"name":"\u0939\u093e\u0907\u092a\u0930\u092c\u094b\u0932\u093e \u0915\u093e \u0938\u092e\u0940\u0915\u0930\u0923 \u0914\u0930 \u0907\u0938\u0915\u093e \u0928\u093f\u0930\u0942\u092a\u0923"}]},{"@type":"WebSite","@id":"http:\/\/toposuranos.com\/material\/#website","url":"http:\/\/toposuranos.com\/material\/","name":"toposuranos.com\/material","description":"","publisher":{"@id":"http:\/\/toposuranos.com\/material\/#organization"},"potentialAction":[{"@type":"SearchAction","target":{"@type":"EntryPoint","urlTemplate":"http:\/\/toposuranos.com\/material\/?s={search_term_string}"},"query-input":{"@type":"PropertyValueSpecification","valueRequired":true,"valueName":"search_term_string"}}],"inLanguage":"es"},{"@type":"Organization","@id":"http:\/\/toposuranos.com\/material\/#organization","name":"toposuranos.com\/material","url":"http:\/\/toposuranos.com\/material\/","logo":{"@type":"ImageObject","inLanguage":"es","@id":"http:\/\/toposuranos.com\/material\/#\/schema\/logo\/image\/","url":"http:\/\/toposuranos.com\/material\/wp-content\/uploads\/2023\/10\/logo.png","contentUrl":"http:\/\/toposuranos.com\/material\/wp-content\/uploads\/2023\/10\/logo.png","width":2400,"height":2059,"caption":"toposuranos.com\/material"},"image":{"@id":"http:\/\/toposuranos.com\/material\/#\/schema\/logo\/image\/"},"sameAs":["https:\/\/www.facebook.com\/groups\/toposuranos","https:\/\/x.com\/topuranos","https:\/\/www.youtube.com\/channel\/UC16yDm12cPcrwsE0fAM7X1g","https:\/\/www.linkedin.com\/company\/69429190"]},{"@type":"Person","@id":"http:\/\/toposuranos.com\/material\/#\/schema\/person\/e15164361c3f9a2a02cf6c234cf7fdc1","name":"giorgio.reveco","image":{"@type":"ImageObject","inLanguage":"es","@id":"http:\/\/toposuranos.com\/material\/#\/schema\/person\/image\/","url":"http:\/\/toposuranos.com\/material\/wp-content\/uploads\/2023\/10\/1694478625378-96x96.jpeg","contentUrl":"http:\/\/toposuranos.com\/material\/wp-content\/uploads\/2023\/10\/1694478625378-96x96.jpeg","caption":"giorgio.reveco"},"description":"Soy Licenciado en F\u00edsica, Magister en Ingenier\u00eda Industrial y Docente Universitario. Me dedico a desmitificar la f\u00edsica y las matem\u00e1ticas. Mi objetivo es hacer que estos campos sean f\u00e1cilmente comprensibles para todos, proporcionando las herramientas para explorar no solo el mundo que nos rodea, sino tambi\u00e9n las profundidades de nuestra propia existencia y el orden natural que nos conecta con el cosmos.","sameAs":["http:\/\/toposuranos.com\/material"],"url":"http:\/\/toposuranos.com\/material\/author\/giorgio-reveco\/"}]}},"_links":{"self":[{"href":"http:\/\/toposuranos.com\/material\/wp-json\/wp\/v2\/posts\/28995","targetHints":{"allow":["GET"]}}],"collection":[{"href":"http:\/\/toposuranos.com\/material\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"http:\/\/toposuranos.com\/material\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"http:\/\/toposuranos.com\/material\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"http:\/\/toposuranos.com\/material\/wp-json\/wp\/v2\/comments?post=28995"}],"version-history":[{"count":0,"href":"http:\/\/toposuranos.com\/material\/wp-json\/wp\/v2\/posts\/28995\/revisions"}],"wp:featuredmedia":[{"embeddable":true,"href":"http:\/\/toposuranos.com\/material\/wp-json\/wp\/v2\/media\/28988"}],"wp:attachment":[{"href":"http:\/\/toposuranos.com\/material\/wp-json\/wp\/v2\/media?parent=28995"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"http:\/\/toposuranos.com\/material\/wp-json\/wp\/v2\/categories?post=28995"},{"taxonomy":"post_tag","embeddable":true,"href":"http:\/\/toposuranos.com\/material\/wp-json\/wp\/v2\/tags?post=28995"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}