{"id":28969,"date":"2021-04-28T13:00:21","date_gmt":"2021-04-28T13:00:21","guid":{"rendered":"http:\/\/toposuranos.com\/material\/?p=28969"},"modified":"2024-09-22T02:01:32","modified_gmt":"2024-09-22T02:01:32","slug":"%e0%a4%a6%e0%a5%80%e0%a4%b0%e0%a5%8d%e0%a4%98%e0%a4%b5%e0%a5%83%e0%a4%a4%e0%a5%8d%e0%a4%a4-%e0%a4%94%e0%a4%b0-%e0%a4%b5%e0%a5%83%e0%a4%a4-%e0%a4%95%e0%a5%80-%e0%a4%b8%e0%a4%ae%e0%a5%80%e0%a4%95","status":"publish","type":"post","link":"https:\/\/toposuranos.com\/material\/hi\/%e0%a4%a6%e0%a5%80%e0%a4%b0%e0%a5%8d%e0%a4%98%e0%a4%b5%e0%a5%83%e0%a4%a4%e0%a5%8d%e0%a4%a4-%e0%a4%94%e0%a4%b0-%e0%a4%b5%e0%a5%83%e0%a4%a4-%e0%a4%95%e0%a5%80-%e0%a4%b8%e0%a4%ae%e0%a5%80%e0%a4%95\/","title":{"rendered":"\u0926\u0940\u0930\u094d\u0918\u0935\u0943\u0924\u094d\u0924 \u0914\u0930 \u0935\u0943\u0924 \u0915\u0940 \u0938\u092e\u0940\u0915\u0930\u0923"},"content":{"rendered":"<p><center><\/p>\n<h1>\u0926\u0940\u0930\u094d\u0918\u0935\u0943\u0924\u094d\u0924 \u0914\u0930 \u0935\u0943\u0924 \u0915\u0940 \u0938\u092e\u0940\u0915\u0930\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 \u0926\u0940\u0930\u094d\u0918\u0935\u0943\u0924\u094d\u0924 \u0915\u0940 \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 \u092a\u094d\u0930\u093e\u092a\u094d\u0924 \u0915\u0930\u0928\u0947 \u0915\u0940 \u092a\u094d\u0930\u0915\u094d\u0930\u093f\u092f\u093e \u0938\u092e\u091d\u093e\u0908 \u0917\u0908 \u0939\u0948, \u091c\u094b \u092f\u0939 \u092c\u0924\u093e\u0924\u0940 \u0939\u0948 \u0915\u093f \u0926\u0940\u0930\u094d\u0918\u0935\u0943\u0924\u094d\u0924 \u092a\u0930 \u0915\u093f\u0938\u0940 \u092d\u0940 \u092c\u093f\u0902\u0926\u0941 \u0938\u0947 \u0926\u094b \u0938\u094d\u0925\u093f\u0930 \u0915\u0947\u0902\u0926\u094d\u0930\u094b\u0902 \u0924\u0915 \u0915\u0940 \u0926\u0942\u0930\u0940 \u0915\u093e \u092f\u094b\u0917 \u0938\u094d\u0925\u093f\u0930 \u0939\u094b\u0924\u093e \u0939\u0948\u0964 \u090f\u0915 \u0935\u093f\u0938\u094d\u0924\u0943\u0924 \u092c\u0940\u091c\u0917\u0923\u093f\u0924\u0940\u092f \u0935\u093f\u0915\u093e\u0938 \u0915\u0947 \u092e\u093e\u0927\u094d\u092f\u092e \u0938\u0947, \u0926\u0940\u0930\u094d\u0918\u0935\u0943\u0924\u094d\u0924 \u0915\u0940 \u0938\u093e\u092e\u093e\u0928\u094d\u092f \u0938\u092e\u0940\u0915\u0930\u0923 \u0914\u0930 \u0909\u0938\u0915\u0940 \u0915\u0948\u0928\u094b\u0928\u093f\u0915\u0932 (\u092e\u093e\u0928\u0915) \u0930\u0942\u092a \u0915\u094b \u092a\u094d\u0930\u093e\u092a\u094d\u0924 \u0915\u093f\u092f\u093e \u091c\u093e\u0924\u093e \u0939\u0948, \u0914\u0930 \u0926\u0940\u0930\u094d\u0918\u0935\u0943\u0924\u094d\u0924 \u0914\u0930 \u0935\u0943\u0924 \u0915\u0947 \u092c\u0940\u091a \u0938\u0902\u092c\u0902\u0927 \u0915\u093e \u092d\u0940 \u092a\u0924\u093e \u091a\u0932\u0924\u093e \u0939\u0948, \u092f\u0939 \u0926\u093f\u0916\u093e\u0924\u0947 \u0939\u0941\u090f \u0915\u093f \u0935\u0943\u0924 \u0924\u092c \u0926\u0940\u0930\u094d\u0918\u0935\u0943\u0924\u094d\u0924 \u0915\u093e \u0935\u093f\u0936\u0947\u0937 \u092e\u093e\u092e\u0932\u093e \u0939\u094b\u0924\u093e \u0939\u0948 \u091c\u092c \u0926\u094b\u0928\u094b\u0902 \u0905\u0930\u094d\u0927-\u0905\u0915\u094d\u0937 \u0938\u092e\u093e\u0928 \u0939\u094b\u0924\u0947 \u0939\u0948\u0902\u0964<br \/>\n   <\/em><\/p>\n<p>   <strong>\u0938\u0940\u0916\u0928\u0947 \u0915\u0947 \u0909\u0926\u094d\u0926\u0947\u0936\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>\u0926\u0940\u0930\u094d\u0918\u0935\u0943\u0924\u094d\u0924 \u0915\u0940 \u0938\u092e\u0940\u0915\u0930\u0923 \u0915\u094b<\/strong> \u0909\u0938\u0915\u0940 \u091c\u094d\u092f\u093e\u092e\u093f\u0924\u0940\u092f \u092a\u0930\u093f\u092d\u093e\u0937\u093e \u0938\u0947 \u092a\u094d\u0930\u093e\u092a\u094d\u0924 \u0915\u0930\u0947\u0902\u0964<\/li>\n<li><strong>\u0926\u0940\u0930\u094d\u0918\u0935\u0943\u0924\u094d\u0924 \u0938\u092e\u0940\u0915\u0930\u0923 \u0915\u0947 \u0938\u093e\u092e\u093e\u0928\u094d\u092f \u0914\u0930 \u0915\u0948\u0928\u094b\u0928\u093f\u0915\u0932 \u0930\u0942\u092a \u0915\u094b \u092a\u0939\u091a\u093e\u0928\u0947\u0902\u0964<\/strong><\/li>\n<\/ol>\n<p>   \u0938\u093e\u092e\u0917\u094d\u0930\u0940 \u0938\u0942\u091a\u0940<br \/>\n   <a href=\"#1\">\u091c\u094d\u092f\u093e\u092e\u093f\u0924\u0940\u092f \u0938\u0942\u0924\u094d\u0930<\/a><br \/>\n   <a href=\"#2\">\u0926\u0940\u0930\u094d\u0918\u0935\u0943\u0924\u094d\u0924 \u0915\u0940 \u0938\u092e\u0940\u0915\u0930\u0923 \u0915\u0940 \u092a\u094d\u0930\u093e\u092a\u094d\u0924\u093f<\/a><br \/>\n   <a href=\"#3\">\u0926\u0940\u0930\u094d\u0918\u0935\u0943\u0924\u094d\u0924 \u0915\u0940 \u0938\u093e\u092e\u093e\u0928\u094d\u092f \u0938\u092e\u0940\u0915\u0930\u0923<\/a><br \/>\n   <a href=\"#4\">\u0926\u0940\u0930\u094d\u0918\u0935\u0943\u0924\u094d\u0924 \u0915\u0940 \u0915\u0948\u0928\u094b\u0928\u093f\u0915\u0932 \u0938\u092e\u0940\u0915\u0930\u0923<\/a><br \/>\n   <a href=\"#5\">\u0935\u0943\u0924 \u0915\u0940 \u0938\u092e\u0940\u0915\u0930\u0923 \u092e\u0947\u0902 \u092a\u0930\u093f\u0935\u0930\u094d\u0924\u0928<\/a>\n   <\/p>\n<p>   <\/center><\/p>\n<p>   <center><iframe class=\"lazyload\" width=\"560\" height=\"315\" data-src=\"https:\/\/www.youtube.com\/embed\/HHiC0bp-Vyc\" title=\"YouTube video player\" frameborder=\"0\" allow=\"accelerometer; autoplay; clipboard-write; encrypted-media; gyroscope; picture-in-picture\" allowfullscreen><\/iframe><\/center><br \/>\n   <a name=\"1\"><\/a><\/p>\n<h2>\u091c\u094d\u092f\u093e\u092e\u093f\u0924\u0940\u092f \u0938\u0942\u0924\u094d\u0930<\/h2>\n<p style=\"text-align: justify;\"><a href=\"https:\/\/www.youtube.com\/watch?v=HHiC0bp-Vyc&amp;t=133s\" target=\"_blank\" rel=\"noopener\"><strong>\u0926\u0940\u0930\u094d\u0918\u0935\u0943\u0924\u094d\u0924 \u0915\u0940 \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 \u0909\u0938\u0940 \u0924\u0930\u0939 \u0938\u0947 \u0938\u094b\u091a\u0928\u0947 \u0915\u0940 \u091c\u093c\u0930\u0942\u0930\u0924 \u0939\u0948 \u091c\u0948\u0938\u0947 <a href=\"https:\/\/toposuranos.com\/la-ecuacion-de-las-parabolas-definiciones-y-propiedades\/\" rel=\"noopener\" target=\"_blank\">\u092a\u0930\u0935\u0932\u092f \u0915\u0947 \u0938\u093e\u0925 \u0915\u093f\u092f\u093e \u0917\u092f\u093e \u0939\u0948\u0964<\/a> \u090f\u0915 \u0926\u0940\u0930\u094d\u0918\u0935\u0943\u0924\u094d\u0924 \u0935\u0939 \u092c\u093f\u0902\u0926\u0941\u0913\u0902 \u0915\u093e \u0938\u0947\u091f \u0939\u0948 \u091c\u093f\u0928\u0915\u0940 \u0926\u094b \u0938\u094d\u0925\u093f\u0930 \u0915\u0947\u0902\u0926\u094d\u0930\u094b\u0902 (\u092b\u094b\u0915\u0938) \u0938\u0947 \u0926\u0942\u0930\u0940 \u0915\u093e \u092f\u094b\u0917 \u0939\u092e\u0947\u0936\u093e \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\/-rHroj77w4-o\/YIhoGfTvE_I\/AAAAAAAAFAw\/2Yoa3Q2yrmknQMPObDz8wuyDoOehCug5QCLcBGAsYHQ\/s0\/elipse.PNG\" alt=\"\u0926\u0940\u0930\u094d\u0918\u0935\u0943\u0924\u094d\u0924\" class=\" aligncenter lazyload\" width=\"338\" height=\"241\" \/><noscript><img decoding=\"async\" src=\"https:\/\/1.bp.blogspot.com\/-rHroj77w4-o\/YIhoGfTvE_I\/AAAAAAAAFAw\/2Yoa3Q2yrmknQMPObDz8wuyDoOehCug5QCLcBGAsYHQ\/s0\/elipse.PNG\" alt=\"\u0926\u0940\u0930\u094d\u0918\u0935\u0943\u0924\u094d\u0924\" class=\" aligncenter lazyload\" width=\"338\" height=\"241\" \/><\/noscript><\/p>\n<p style=\"text-align: justify;\">\u0905\u0930\u094d\u0925\u093e\u0924\u094d, \u092f\u0939 \u092a\u0942\u0930\u093e \u0939\u094b\u0917\u093e:<\/p>\n<p style=\"text-align: center;\"><span class=\"katex-eq\" data-katex-display=\"false\">d(f_1,p) + d(f_2,p) = \u0938\u094d\u0925\u093f\u0930<\/span>\n<p>   <a name=\"2\"><\/a><\/p>\n<h2>\u0926\u0940\u0930\u094d\u0918\u0935\u0943\u0924\u094d\u0924 \u0915\u0940 \u0938\u092e\u0940\u0915\u0930\u0923 \u0915\u0940 \u092a\u094d\u0930\u093e\u092a\u094d\u0924\u093f<\/h2>\n<p style=\"text-align: justify;\"><a href=\"https:\/\/www.youtube.com\/watch?v=HHiC0bp-Vyc&amp;t=311s\" target=\"_blank\" rel=\"noopener\"><strong>\u091c\u094d\u092f\u093e\u092e\u093f\u0924\u0940\u092f \u092a\u0930\u093f\u092d\u093e\u0937\u093e \u0915\u0947 \u0906\u0927\u093e\u0930 \u092a\u0930<\/strong><\/a> \u0939\u092e \u090f\u0915 \u092c\u0940\u091c\u0917\u0923\u093f\u0924\u0940\u092f \u0938\u092e\u0940\u0915\u0930\u0923 \u092a\u094d\u0930\u093e\u092a\u094d\u0924 \u0915\u0930 \u0938\u0915\u0924\u0947 \u0939\u0948\u0902 \u091c\u094b \u0907\u0938\u0947 \u0935\u0930\u094d\u0923\u093f\u0924 \u0915\u0930\u0924\u093e \u0939\u0948\u0964 \u0910\u0938\u093e \u0915\u0930\u0928\u0947 \u0915\u0947 \u0932\u093f\u090f, \u0939\u092e \u0915\u0941\u091b \u0938\u0930\u0932 \u092e\u093e\u0928\u094d\u092f\u0924\u093e\u0913\u0902 \u0915\u093e \u0909\u092a\u092f\u094b\u0917 \u0915\u0930\u0947\u0902\u0917\u0947\u0964 \u0939\u092e \u092e\u093e\u0928\u0924\u0947 \u0939\u0948\u0902 \u0915\u093f \u0915\u0947\u0902\u0926\u094d\u0930 <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> \u092a\u0930 \u0938\u094d\u0925\u093f\u0924 \u0939\u0948\u0902, \u0914\u0930 \u0907\u0938 \u092a\u094d\u0930\u0915\u093e\u0930 \u0915\u094b\u0908 \u092d\u0940 \u092c\u093f\u0902\u0926\u0941 <span class=\"katex-eq\" data-katex-display=\"false\">p=(x,y)<\/span> \u092f\u0926\u093f \u0926\u0940\u0930\u094d\u0918\u0935\u0943\u0924\u094d\u0924 \u0915\u093e \u0939\u093f\u0938\u094d\u0938\u093e \u0939\u0948, \u0924\u094b \u092f\u0939 \u0938\u092e\u0940\u0915\u0930\u0923 \u092a\u0942\u0930\u093e \u0939\u094b\u0917\u093e:<\/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>   <img decoding=\"async\" src=\"data:image\/gif;base64,R0lGODlhAQABAIAAAAAAAP\/\/\/yH5BAEAAAAALAAAAAABAAEAAAIBRAA7\" data-src=\"https:\/\/1.bp.blogspot.com\/-LtAamnh5D78\/YIiBshjM70I\/AAAAAAAAFA4\/hGiHx6jf_nMOOUHfH-Ywj34TyDJDGEv-wCLcBGAsYHQ\/s0\/ecuacion%2Bde%2Blas%2Belipses.PNG\" alt=\"\u0926\u0940\u0930\u094d\u0918\u0935\u0943\u0924\u094d\u0924 \u0915\u0940 \u0938\u092e\u0940\u0915\u0930\u0923\" class=\" aligncenter lazyload\" width=\"412\" height=\"333\" \/><noscript><img decoding=\"async\" src=\"https:\/\/1.bp.blogspot.com\/-LtAamnh5D78\/YIiBshjM70I\/AAAAAAAAFA4\/hGiHx6jf_nMOOUHfH-Ywj34TyDJDGEv-wCLcBGAsYHQ\/s0\/ecuacion%2Bde%2Blas%2Belipses.PNG\" alt=\"\u0926\u0940\u0930\u094d\u0918\u0935\u0943\u0924\u094d\u0924 \u0915\u0940 \u0938\u092e\u0940\u0915\u0930\u0923\" class=\" aligncenter lazyload\" width=\"412\" height=\"333\" \/><\/noscript><\/p>\n<p style=\"text-align: justify;\">\u091c\u0939\u093e\u0901 <span class=\"katex-eq\" data-katex-display=\"false\">a\\in\\mathbb{R}<\/span> \u090f\u0915 \u0938\u094d\u0925\u093f\u0930 \u092e\u093e\u0928 \u0939\u0948\u0964 \u092f\u0939\u093e\u0901 \u0938\u0947, \u0939\u092e \u0928\u093f\u092e\u094d\u0928\u0932\u093f\u0916\u093f\u0924 \u0924\u0930\u094d\u0915 \u0935\u093f\u0915\u0938\u093f\u0924 \u0915\u0930 \u0938\u0915\u0924\u0947 \u0939\u0948\u0902:<\/p>\n<table style=\"text-align: justify;\">\n<tbody>\n<tr>\n<td width=\"50\">(1)<\/td>\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>; \u0926\u0940\u0930\u094d\u0918\u0935\u0943\u0924\u094d\u0924 \u0915\u0940 \u091c\u094d\u092f\u093e\u092e\u093f\u0924\u0940\u092f \u092a\u0930\u093f\u092d\u093e\u0937\u093e<\/td>\n<\/tr>\n<tr>\n<td><\/td>\n<td><span class=\"katex-eq\" data-katex-display=\"false\">\\sqrt{(x-c)^2 + y^2} = 2a - \\sqrt{(x+c)^2 + y^2}<\/span><\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td>(2)<\/td>\n<td><span class=\"katex-eq\" data-katex-display=\"false\">(x-c)^2 + \\cancel{y^2} = 4a^2 -4a \\sqrt{(x+c)^2 + y^2} + (x+c)^2 + \\cancel{y^2}<\/span><\/td>\n<td>; (1) \u0915\u093e \u0935\u0930\u094d\u0917<\/td>\n<\/tr>\n<tr>\n<td><\/td>\n<td><span class=\"katex-eq\" data-katex-display=\"false\">(x-c)^2 = 4a^2 -4a \\sqrt{(x+c)^2 + y^2} + (x+c)^2 <\/span><\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td><\/td>\n<td><span class=\"katex-eq\" data-katex-display=\"false\">\\cancel{x^2} -2xc + \\cancel{c^2} = 4a^2 -4a \\sqrt{(x+c)^2 + y^2} + \\cancel{x^2} +2xc + \\cancel{c^2} <\/span><\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td><\/td>\n<td><span class=\"katex-eq\" data-katex-display=\"false\">-2xc = 4a^2 -4a \\sqrt{(x+c)^2 + y^2} +2xc <\/span><\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td><\/td>\n<td><span class=\"katex-eq\" data-katex-display=\"false\">4a \\sqrt{(x+c)^2 + y^2} = 4a^2 +4xc = 4(a^2 + xc) <\/span><\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td><\/td>\n<td><span class=\"katex-eq\" data-katex-display=\"false\">a \\sqrt{(x+c)^2 + y^2} = a^2 + xc <\/span><\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td>(3)<\/td>\n<td><span class=\"katex-eq\" data-katex-display=\"false\">a^2 [(x+c)^2 + y^2] = (a^2 + xc)^2 <\/span><\/td>\n<td>; (2) \u0915\u093e \u0935\u0930\u094d\u0917<\/td>\n<\/tr>\n<tr>\n<td><\/td>\n<td><span class=\"katex-eq\" data-katex-display=\"false\">a^2 [x^2 + 2xc + c2 + y^2] = a^4 +2a^2xc + x^2c^2 <\/span><\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td><\/td>\n<td><span class=\"katex-eq\" data-katex-display=\"false\"> a^2 x^2 + \\cancel{2xca^2} + a^2 c2 + a^2 y^2 = a^4 + \\cancel{2a^2xc} + x^2c^2 <\/span><\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td><\/td>\n<td><span class=\"katex-eq\" data-katex-display=\"false\"> a^2 x^2 + a^2 c2 + a^2 y^2 = a^4 + x^2c^2 <\/span><\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td><\/td>\n<td><span class=\"katex-eq\" data-katex-display=\"false\"> x^2 (a^2 - c^2) + a^2 y^2 = a^4 - a^2 c^2 =a^2(a^2-c^2) <\/span><\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td><\/td>\n<td><span class=\"katex-eq\" data-katex-display=\"false\"> \\dfrac{x^2}{a^2} +\\dfrac{ y^2}{a^2-c^2} = 1 <\/span><\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td>(4)<\/td>\n<td><span class=\"katex-eq\" data-katex-display=\"false\">0\\lt a^2 - c^2 =: b^2 <\/span><\/td>\n<td>; <span class=\"katex-eq\" data-katex-display=\"false\">b^2<\/span> \u0915\u093e \u092e\u093e\u0928 \u0938\u0915\u093e\u0930\u093e\u0924\u094d\u092e\u0915 \u0939\u0948, \u091c\u0948\u0938\u093e \u0915\u093f \u0906\u0915\u0943\u0924\u093f \u092e\u0947\u0902 \u0926\u093f\u0916\u093e\u092f\u093e \u0917\u092f\u093e \u0939\u0948\u0964<\/td>\n<\/tr>\n<tr>\n<td>(5)<\/td>\n<td><span class=\"katex-eq\" data-katex-display=\"false\">{\\dfrac{x^2}{a^2} +\\dfrac{ y^2}{b^2} = 1}<\/span><\/td>\n<td>; (3) \u0914\u0930 (4) \u0938\u0947<\/td>\n<\/tr>\n<tr>\n<td><\/td>\n<td><span class=\"katex-eq\" data-katex-display=\"false\">\\boxed{\\left(\\dfrac{x}{a}\\right)^2 + \\left(\\dfrac{y}{b}\\right)^2 = 1}<\/span><\/td>\n<td><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p style=\"text-align: center;\">\u092f\u0939 \u0926\u0940\u0930\u094d\u0918\u0935\u0943\u0924\u094d\u0924 \u0915\u0940 \u00ab\u0938\u092e\u0940\u0915\u0930\u0923\u00bb \u0939\u0948\u0964<\/p>\n<p>   <a name=\"3\"><\/a><\/p>\n<h2>\u0926\u0940\u0930\u094d\u0918\u0935\u0943\u0924\u094d\u0924 \u0915\u0940 \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=HHiC0bp-Vyc&amp;t=706s\" target=\"_blank\" rel=\"noopener\"><strong>\u091c\u094b \u0938\u092e\u0940\u0915\u0930\u0923 \u0939\u092e\u0928\u0947 \u0905\u092d\u0940 \u092a\u094d\u0930\u093e\u092a\u094d\u0924 \u0915\u093f\u092f\u093e \u0939\u0948<\/strong><\/a> \u0909\u0938\u0947 \u0939\u092e \u0905\u0928\u0941\u0935\u093e\u0926 \u0930\u0942\u092a\u093e\u0902\u0924\u0930 \u0926\u094d\u0935\u093e\u0930\u093e \u0909\u0938\u0915\u0940 \u0938\u093e\u092e\u093e\u0928\u094d\u092f \u0930\u0942\u092a \u092e\u0947\u0902 \u0932\u093e \u0938\u0915\u0924\u0947 \u0939\u0948\u0902, \u091c\u0939\u093e\u0901 \u0939\u092e \u092a\u094d\u0930\u0924\u093f\u0938\u094d\u0925\u093e\u092a\u0928 \u0915\u0930\u0924\u0947 \u0939\u0948\u0902 <span class=\"katex-eq\" data-katex-display=\"false\">x\\longmapsto (x-h)<\/span> \u0914\u0930 <span class=\"katex-eq\" data-katex-display=\"false\">y\\longmapsto (y-k).<\/span> \u0907\u0938\u0938\u0947 \u0939\u092e\u0947\u0902 \u0926\u0940\u0930\u094d\u0918\u0935\u0943\u0924\u094d\u0924 \u0915\u0940 \u0938\u093e\u092e\u093e\u0928\u094d\u092f \u0938\u092e\u0940\u0915\u0930\u0923 \u092a\u094d\u0930\u093e\u092a\u094d\u0924 \u0939\u094b\u0924\u0940 \u0939\u0948:<\/p>\n<p style=\"text-align: center;\"><span class=\"katex-eq\" data-katex-display=\"false\">\\boxed{\\left(\\dfrac{x-h}{a}\\right)^2 + \\left(\\dfrac{y-k}{b}\\right)^2 = 1}<\/span>\n<p style=\"text-align: justify;\">\u092f\u0939 <span class=\"katex-eq\" data-katex-display=\"false\">(h,k)<\/span> \u092a\u0930 \u0915\u0947\u0902\u0926\u094d\u0930\u093f\u0924 \u090f\u0915 \u0926\u0940\u0930\u094d\u0918\u0935\u0943\u0924\u094d\u0924 \u0939\u0948\u0964<\/p>\n<p>   <img decoding=\"async\" src=\"data:image\/gif;base64,R0lGODlhAQABAIAAAAAAAP\/\/\/yH5BAEAAAAALAAAAAABAAEAAAIBRAA7\" data-src=\"https:\/\/1.bp.blogspot.com\/-lkxt91FvMTs\/YIiQaL9wpII\/AAAAAAAAFBA\/sUxc6ajd6tcPymC8g4oh3M0l2CTI-xOvgCLcBGAsYHQ\/s0\/elipsegeneral.PNG\" alt=\"\u0938\u093e\u092e\u093e\u0928\u094d\u092f \u0926\u0940\u0930\u094d\u0918\u0935\u0943\u0924\u094d\u0924\" class=\" aligncenter lazyload\" width=\"469\" height=\"373\" \/><noscript><img decoding=\"async\" src=\"https:\/\/1.bp.blogspot.com\/-lkxt91FvMTs\/YIiQaL9wpII\/AAAAAAAAFBA\/sUxc6ajd6tcPymC8g4oh3M0l2CTI-xOvgCLcBGAsYHQ\/s0\/elipsegeneral.PNG\" alt=\"\u0938\u093e\u092e\u093e\u0928\u094d\u092f \u0926\u0940\u0930\u094d\u0918\u0935\u0943\u0924\u094d\u0924\" class=\" aligncenter lazyload\" width=\"469\" height=\"373\" \/><\/noscript><br \/>\n   <a name=\"4\"><\/a><\/p>\n<h2>\u0926\u0940\u0930\u094d\u0918\u0935\u0943\u0924\u094d\u0924 \u0915\u0940 \u0915\u0948\u0928\u094b\u0928\u093f\u0915\u0932 \u0938\u092e\u0940\u0915\u0930\u0923<\/h2>\n<p style=\"text-align: justify;\"><a href=\"https:\/\/www.youtube.com\/watch?v=HHiC0bp-Vyc&amp;t=761s\" target=\"_blank\" rel=\"noopener\"><strong>\u0907\u0938 \u092a\u0930 \u092c\u0940\u091c\u0917\u0923\u093f\u0924\u0940\u092f \u0935\u093f\u0915\u093e\u0938 \u0915\u0930\u0924\u0947 \u0939\u0941\u090f,<\/strong><\/a> \u0939\u092e \u0926\u0940\u0930\u094d\u0918\u0935\u0943\u0924\u094d\u0924 \u0915\u0940 \u0915\u0948\u0928\u094b\u0928\u093f\u0915\u0932 \u0938\u092e\u0940\u0915\u0930\u0923 \u092a\u0930 \u092a\u0939\u0941\u0902\u091a\u0924\u0947 \u0939\u0948\u0902:<\/p>\n<table style=\"text-align: justify;\">\n<tbody>\n<tr>\n<td width=\"50\">(1)<\/td>\n<td><span class=\"katex-eq\" data-katex-display=\"false\">\\left(\\dfrac{x-h}{a}\\right)^2 + \\left(\\dfrac{y-k}{b}\\right)^2 = 1<\/span><\/td>\n<td>; \u0926\u0940\u0930\u094d\u0918\u0935\u0943\u0924\u094d\u0924 \u0915\u0940 \u0938\u093e\u092e\u093e\u0928\u094d\u092f \u0938\u092e\u0940\u0915\u0930\u0923<\/td>\n<\/tr>\n<tr>\n<td><\/td>\n<td><span class=\"katex-eq\" data-katex-display=\"false\">b^2 (x-h)^2 + a^2(y-k)^2 = a^2 b^2<\/span><\/td>\n<td>; <span class=\"katex-eq\" data-katex-display=\"false\">a^2b^2<\/span> \u0938\u0947 \u0917\u0941\u0923\u093e \u0915\u0930\u0947\u0902<\/td>\n<\/tr>\n<tr>\n<td><\/td>\n<td><span class=\"katex-eq\" data-katex-display=\"false\">b^2 [x^2-2xh+h^2] + a^2[y^2-2yk + k^2] = a^2 b^2<\/span><\/td>\n<td>; \u0935\u0930\u094d\u0917\u094b\u0902 \u0915\u093e \u0935\u093f\u0938\u094d\u0924\u093e\u0930 \u0915\u0930\u0947\u0902<\/td>\n<\/tr>\n<tr>\n<td><\/td>\n<td><span class=\"katex-eq\" data-katex-display=\"false\"> b^2 x^2-2hb^2 x + h^2b^2 + a^2 y^2-2ka^2y + k^2a^2 = a^2 b^2<\/span><\/td>\n<td>; \u0915\u094b\u0937\u094d\u0920\u0915 \u0915\u093e \u0935\u093f\u0938\u094d\u0924\u093e\u0930 \u0915\u0930\u0947\u0902<\/td>\n<\/tr>\n<tr>\n<td><\/td>\n<td><span class=\"katex-eq\" data-katex-display=\"false\"> b^2 x^2- 2hb^2 x + a^2 y^2-2ka^2y +(h^2b^2 + k^2a^2 - a^2 b^2) = 0 <\/span><\/td>\n<td>; \u0938\u094d\u0925\u093f\u0930\u093e\u0902\u0936\u094b\u0902 \u0915\u094b \u091c\u094b\u0921\u093c\u0947\u0902<\/td>\n<\/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 \u092e\u0947\u0902, \u0939\u092e \u092a\u094d\u0930\u0924\u093f\u0938\u094d\u0925\u093e\u092a\u0928 \u0915\u0930 \u0938\u0915\u0924\u0947 \u0939\u0948\u0902 <span class=\"katex-eq\" data-katex-display=\"false\">A:=b^2,<\/span> <span class=\"katex-eq\" data-katex-display=\"false\">B:=-2hb^2,<\/span> <span class=\"katex-eq\" data-katex-display=\"false\">C:=a^2,<\/span> <span class=\"katex-eq\" data-katex-display=\"false\">D:=-2ka^2<\/span> \u0914\u0930 <span class=\"katex-eq\" data-katex-display=\"false\">E:=h^2b^2 + k^2a^2 - a^2 b^2.<\/span> \u0907\u0938 \u092a\u094d\u0930\u0915\u093e\u0930, \u0939\u092e \u0926\u0947\u0916 \u0938\u0915\u0924\u0947 \u0939\u0948\u0902 \u0915\u093f \u0926\u0940\u0930\u094d\u0918\u0935\u0943\u0924\u094d\u0924 \u0915\u0940 \u0938\u092e\u0940\u0915\u0930\u0923 \u0907\u0938 \u0930\u0942\u092a \u092e\u0947\u0902 \u0935\u094d\u092f\u0915\u094d\u0924 \u0915\u0940 \u091c\u093e \u0938\u0915\u0924\u0940 \u0939\u0948:<\/p>\n<p style=\"text-align: center;\"><span class=\"katex-eq\" data-katex-display=\"false\">Ax^2 + Bx + Cy^2 + Dy + E = 0<\/span>\n<p style=\"text-align: justify;\">\u092f\u0939 \u0935\u0939\u0940 \u0939\u0948 \u091c\u093f\u0938\u0947 \u0939\u092e \u00ab\u0926\u0940\u0930\u094d\u0918\u0935\u0943\u0924\u094d\u0924 \u0915\u0940 \u0915\u0948\u0928\u094b\u0928\u093f\u0915\u0932 \u0938\u092e\u0940\u0915\u0930\u0923\u00bb \u0915\u0939\u0924\u0947 \u0939\u0948\u0902\u0964<\/p>\n<p style=\"text-align: justify;\">\u0907\u0928 \u0935\u093f\u0915\u093e\u0938\u094b\u0902 \u0938\u0947, \u0939\u092e \u0915\u0948\u0928\u094b\u0928\u093f\u0915\u0932 \u0938\u092e\u0940\u0915\u0930\u0923 \u0915\u0940 \u0938\u094d\u0925\u093f\u0930\u093e\u0902\u0915\u094b\u0902 \u092a\u0930 \u0915\u0941\u091b \u092a\u094d\u0930\u0924\u093f\u092c\u0902\u0927 \u0928\u093f\u0915\u093e\u0932 \u0938\u0915\u0924\u0947 \u0939\u0948\u0902\u0964 \u0938\u092c\u0938\u0947 \u092e\u0939\u0924\u094d\u0935\u092a\u0942\u0930\u094d\u0923 \u092f\u0939 \u0939\u0948 \u0915\u093f <span class=\"katex-eq\" data-katex-display=\"false\">A<\/span> \u0914\u0930 <span class=\"katex-eq\" data-katex-display=\"false\">B<\/span> \u0915\u093e \u091a\u093f\u0939\u094d\u0928 \u0938\u092e\u093e\u0928 \u0939\u094b\u0928\u093e \u091a\u093e\u0939\u093f\u090f; \u0905\u0928\u094d\u092f\u0925\u093e, \u092f\u0939 \u0926\u0940\u0930\u094d\u0918\u0935\u0943\u0924\u094d\u0924 \u0928\u0939\u0940\u0902 \u092c\u0932\u094d\u0915\u093f \u090f\u0915 \u092a\u0930\u0935\u0932\u092f \u0939\u094b\u0917\u093e\u0964 \u0915\u0948\u0928\u094b\u0928\u093f\u0915\u0932 \u0930\u0942\u092a \u092e\u0947\u0902 \u0914\u0930 \u092d\u0940 \u092a\u094d\u0930\u0924\u093f\u092c\u0902\u0927 \u0939\u094b\u0924\u0947 \u0939\u0948\u0902, \u0932\u0947\u0915\u093f\u0928 \u0909\u0928\u094d\u0939\u0947\u0902 \u0905\u092c \u0926\u0947\u0916\u0928\u093e \u092a\u094d\u0930\u092d\u093e\u0935\u0940 \u0928\u0939\u0940\u0902 \u0939\u0948; \u0939\u092e \u0907\u0928\u094d\u0939\u0947\u0902 \u0935\u093f\u0938\u094d\u0924\u093e\u0930 \u0938\u0947 \u0924\u092c \u0926\u0947\u0916\u0947\u0902\u0917\u0947 \u091c\u092c \u0939\u092e \u0926\u0940\u0930\u094d\u0918\u0935\u0943\u0924\u094d\u0924 \u0914\u0930 \u092a\u0930\u0935\u0932\u092f \u0915\u0940 \u092a\u0939\u091a\u093e\u0928 \u0915\u0930\u0947\u0902\u0917\u0947\u0964<\/p>\n<p>   <a name=\"5\"><\/a><\/p>\n<h2>\u0935\u0943\u0924 \u0915\u0940 \u0938\u092e\u0940\u0915\u0930\u0923 \u092e\u0947\u0902 \u092a\u0930\u093f\u0935\u0930\u094d\u0924\u0928<\/h2>\n<p style=\"text-align: justify;\"><a href=\"https:\/\/www.youtube.com\/watch?v=HHiC0bp-Vyc&amp;t=948s\" target=\"_blank\" rel=\"noopener\"><strong>\u091c\u092c \u0939\u092e \u0926\u0940\u0930\u094d\u0918\u0935\u0943\u0924\u094d\u0924 \u0915\u0940 \u092a\u0939\u091a\u093e\u0928 \u0915\u0947 \u092c\u093e\u0930\u0947 \u092e\u0947\u0902 \u092c\u093e\u0924 \u0915\u0930\u0947\u0902\u0917\u0947,<\/strong><\/a> \u0924\u092c \u0939\u092e \u0926\u0947\u0916\u0947\u0902\u0917\u0947 \u0915\u093f \u0926\u0940\u0930\u094d\u0918\u0935\u0943\u0924\u094d\u0924 \u0915\u0940 \u0938\u093e\u092e\u093e\u0928\u094d\u092f \u0938\u092e\u0940\u0915\u0930\u0923 \u092e\u0947\u0902 \u0938\u094d\u0925\u093f\u0930\u093e\u0902\u0915\u0947 <span class=\"katex-eq\" data-katex-display=\"false\">a<\/span> \u0914\u0930 <span class=\"katex-eq\" data-katex-display=\"false\">b<\/span> \u0915\u094d\u0930\u092e\u0936\u0903 \u0905\u0930\u094d\u0927-\u0905\u0915\u094d\u0937 \u0939\u094b\u0924\u0947 \u0939\u0948\u0902\u0964 \u092f\u0926\u093f \u0939\u092e \u0926\u094b\u0928\u094b\u0902 \u0905\u0930\u094d\u0927-\u0905\u0915\u094d\u0937\u094b\u0902 \u0915\u094b \u0938\u092e\u093e\u0928 \u0915\u0930 \u0926\u0947\u0902, \u0905\u0930\u094d\u0925\u093e\u0924\u094d <span class=\"katex-eq\" data-katex-display=\"false\">a=b=r,<\/span> \u0924\u094b \u0926\u0940\u0930\u094d\u0918\u0935\u0943\u0924\u094d\u0924 \u090f\u0915 \u0935\u0943\u0924 \u092c\u0928 \u091c\u093e\u090f\u0917\u0940, \u091c\u093f\u0938\u0915\u093e \u0924\u094d\u0930\u093f\u091c\u094d\u092f\u093e <span class=\"katex-eq\" data-katex-display=\"false\">r<\/span> \u0939\u094b\u0917\u093e\u0964<\/p>\n<h3>\u0935\u0943\u0924 \u0915\u0940 \u0938\u093e\u092e\u093e\u0928\u094d\u092f \u0938\u092e\u0940\u0915\u0930\u0923<\/h3>\n<p style=\"text-align: justify;\">\u0907\u0938 \u092a\u094d\u0930\u0915\u093e\u0930 \u0939\u092e\u0947\u0902 \u0935\u0943\u0924 \u0915\u0940 \u0938\u093e\u092e\u093e\u0928\u094d\u092f \u0938\u092e\u0940\u0915\u0930\u0923 \u092a\u094d\u0930\u093e\u092a\u094d\u0924 \u0939\u094b\u0924\u0940 \u0939\u0948:<\/p>\n<p style=\"text-align: justify;\"><span class=\"katex-eq\" data-katex-display=\"false\">(x-h)^2 + (y-k)^2 = r^2<\/span>\n<h3>\u0935\u0943\u0924 \u0915\u0940 \u0915\u0948\u0928\u094b\u0928\u093f\u0915\u0932 \u0938\u092e\u0940\u0915\u0930\u0923<\/h3>\n<p style=\"text-align: justify;\">\u0907\u0938\u0940 \u0924\u0930\u0939 \u0938\u0947, \u0939\u092e \u0935\u0943\u0924 \u0915\u0940 \u0915\u0948\u0928\u094b\u0928\u093f\u0915\u0932 \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: justify;\"><span class=\"katex-eq\" data-katex-display=\"false\">Ax^2 + Bx + Cy^2 + Dy + E = 0<\/span>\n<p style=\"text-align: justify;\">\u0907\u0938\u0915\u0940 \u0915\u0948\u0928\u094b\u0928\u093f\u0915\u0932 \u0930\u0942\u092a \u092e\u0947\u0902, \u092f\u0939 \u0926\u0940\u0930\u094d\u0918\u0935\u0943\u0924\u094d\u0924 \u0915\u0947 \u0938\u093e\u0925 \u092e\u0947\u0932 \u0916\u093e\u0924\u093e \u0939\u0948, \u0915\u094d\u092f\u094b\u0902\u0915\u093f \u0935\u0943\u0924, \u091c\u0948\u0938\u093e \u0915\u093f \u0939\u092e\u0928\u0947 \u0926\u0947\u0916\u093e \u0939\u0948, \u0926\u0940\u0930\u094d\u0918\u0935\u0943\u0924\u094d\u0924 \u0915\u093e \u0935\u093f\u0936\u0947\u0937 \u092e\u093e\u092e\u0932\u093e \u0939\u0948\u0964<\/p>\n","protected":false},"excerpt":{"rendered":"<p>\u0926\u0940\u0930\u094d\u0918\u0935\u0943\u0924\u094d\u0924 \u0914\u0930 \u0935\u0943\u0924 \u0915\u0940 \u0938\u092e\u0940\u0915\u0930\u0923 \u0938\u093e\u0930\u093e\u0902\u0936: \u0907\u0938 \u0915\u0915\u094d\u0937\u093e \u092e\u0947\u0902 \u0926\u0940\u0930\u094d\u0918\u0935\u0943\u0924\u094d\u0924 \u0915\u0940 \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 \u092a\u094d\u0930\u093e\u092a\u094d\u0924 \u0915\u0930\u0928\u0947 \u0915\u0940 \u092a\u094d\u0930\u0915\u094d\u0930\u093f\u092f\u093e \u0938\u092e\u091d\u093e\u0908 \u0917\u0908 \u0939\u0948, \u091c\u094b \u092f\u0939 \u092c\u0924\u093e\u0924\u0940 \u0939\u0948 \u0915\u093f \u0926\u0940\u0930\u094d\u0918\u0935\u0943\u0924\u094d\u0924 \u092a\u0930 \u0915\u093f\u0938\u0940 \u092d\u0940 \u092c\u093f\u0902\u0926\u0941 \u0938\u0947 \u0926\u094b \u0938\u094d\u0925\u093f\u0930 \u0915\u0947\u0902\u0926\u094d\u0930\u094b\u0902 \u0924\u0915 \u0915\u0940 \u0926\u0942\u0930\u0940 \u0915\u093e \u092f\u094b\u0917 \u0938\u094d\u0925\u093f\u0930 \u0939\u094b\u0924\u093e \u0939\u0948\u0964 \u090f\u0915 \u0935\u093f\u0938\u094d\u0924\u0943\u0924 \u092c\u0940\u091c\u0917\u0923\u093f\u0924\u0940\u092f \u0935\u093f\u0915\u093e\u0938 \u0915\u0947 \u092e\u093e\u0927\u094d\u092f\u092e \u0938\u0947, \u0926\u0940\u0930\u094d\u0918\u0935\u0943\u0924\u094d\u0924 \u0915\u0940 [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":28959,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"iawp_total_views":0,"footnotes":""},"categories":[577,593],"tags":[],"class_list":["post-28969","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 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content=\"\u0926\u0940\u0930\u094d\u0918\u0935\u0943\u0924\u094d\u0924 \u0915\u0940 \u0938\u092e\u0940\u0915\u0930\u0923 \u0914\u0930 \u0909\u0938\u0915\u0940 \u0935\u0943\u0924 \u0915\u0947 \u0938\u093e\u0925 \u0938\u092e\u094d\u092c\u0902\u0927 \u0915\u094b \u0938\u092e\u091d\u0947\u0902\u0964 \u091c\u093e\u0928\u093f\u090f \u0915\u0948\u0938\u0947 \u091c\u094d\u092f\u093e\u092e\u093f\u0924\u0940\u092f \u092a\u0930\u093f\u092d\u093e\u0937\u093e \u0914\u0930 \u092c\u0940\u091c\u0917\u0923\u093f\u0924\u0940\u092f \u0938\u0930\u0932\u0940\u0915\u0930\u0923\u094b\u0902 \u0915\u093e \u0909\u092a\u092f\u094b\u0917 \u0915\u0930\u0915\u0947 \u0907\u0928 \u0906\u0915\u0943\u0924\u093f\u092f\u094b\u0902 \u0915\u0947 \u0938\u093e\u092e\u093e\u0928\u094d\u092f \u0914\u0930 \u0915\u0948\u0928\u094b\u0928\u093f\u0915\u0932 \u0930\u0942\u092a\u094b\u0902 \u0915\u094b \u092a\u094d\u0930\u093e\u092a\u094d\u0924 \u0915\u093f\u092f\u093e \u091c\u093e \u0938\u0915\u0924\u093e \u0939\u0948\u0964\" 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