{"id":29001,"date":"2021-05-05T13:00:08","date_gmt":"2021-05-05T13:00:08","guid":{"rendered":"http:\/\/toposuranos.com\/material\/?p=29001"},"modified":"2024-09-22T01:54:25","modified_gmt":"2024-09-22T01:54:25","slug":"%d9%85%d8%b9%d8%a7%d8%af%d9%84%d8%a9-%d8%a7%d9%84%d9%82%d8%b7%d9%88%d8%b9-%d8%a7%d9%84%d8%b2%d8%a7%d8%a6%d8%af%d8%a9-%d9%88%d8%a7%d8%b3%d8%aa%d9%86%d8%aa%d8%a7%d8%ac%d9%87%d8%a7","status":"publish","type":"post","link":"http:\/\/toposuranos.com\/material\/ar\/%d9%85%d8%b9%d8%a7%d8%af%d9%84%d8%a9-%d8%a7%d9%84%d9%82%d8%b7%d9%88%d8%b9-%d8%a7%d9%84%d8%b2%d8%a7%d8%a6%d8%af%d8%a9-%d9%88%d8%a7%d8%b3%d8%aa%d9%86%d8%aa%d8%a7%d8%ac%d9%87%d8%a7\/","title":{"rendered":"\u0645\u0639\u0627\u062f\u0644\u0629 \u0627\u0644\u0642\u0637\u0648\u0639 \u0627\u0644\u0632\u0627\u0626\u062f\u0629 \u0648\u0627\u0633\u062a\u0646\u062a\u0627\u062c\u0647\u0627"},"content":{"rendered":"<p><center><\/p>\n<h1>\u0645\u0639\u0627\u062f\u0644\u0629 \u0627\u0644\u0642\u0637\u0648\u0639 \u0627\u0644\u0632\u0627\u0626\u062f\u0629 \u0648\u0627\u0633\u062a\u0646\u062a\u0627\u062c\u0647\u0627<\/h1>\n<p><em><strong>\u0627\u0644\u0645\u0644\u062e\u0635:<\/strong><br \/>\n\u0641\u064a \u0647\u0630\u0627 \u0627\u0644\u062f\u0631\u0633\u060c \u0633\u0646\u0633\u062a\u0643\u0634\u0641 \u0627\u0644\u062a\u0639\u0631\u064a\u0641 \u0627\u0644\u0647\u0646\u062f\u0633\u064a \u0644\u0644\u0642\u0637\u0639 \u0627\u0644\u0632\u0627\u0626\u062f\u060c \u0648\u0646\u0642\u0627\u0631\u0646\u0647 \u0628\u0627\u0644\u0642\u0637\u0639 \u0627\u0644\u0646\u0627\u0642\u0635\u060c \u0648\u0633\u0646\u0633\u062a\u0646\u062a\u062c \u0645\u0639\u0627\u062f\u0644\u062a\u0647 \u0627\u0644\u0639\u0627\u0645\u0629 \u0648\u0627\u0644\u0642\u064a\u0627\u0633\u064a\u0629.<br \/>\n   <\/em><\/p>\n<p>   <strong>\u0623\u0647\u062f\u0627\u0641 \u0627\u0644\u062a\u0639\u0644\u0645:<\/strong><br \/>\n   \u0641\u064a \u0646\u0647\u0627\u064a\u0629 \u0647\u0630\u0627 \u0627\u0644\u062f\u0631\u0633\u060c \u0633\u064a\u0643\u0648\u0646 \u0627\u0644\u0637\u0627\u0644\u0628 \u0642\u0627\u062f\u0631\u064b\u0627 \u0639\u0644\u0649:<\/p>\n<ol style=\"text-align:left;\">\n<li><strong>\u062a\u0639\u0631\u064a\u0641<\/strong> \u0645\u0627\u0647\u064a\u0629 \u0627\u0644\u0642\u0637\u0639 \u0627\u0644\u0632\u0627\u0626\u062f \u0645\u0646 \u0627\u0644\u0646\u0627\u062d\u064a\u0629 \u0627\u0644\u0647\u0646\u062f\u0633\u064a\u0629.<\/li>\n<li><strong>\u0627\u0633\u062a\u0646\u062a\u0627\u062c<\/strong> \u0627\u0644\u0645\u0639\u0627\u062f\u0644\u0629 \u0627\u0644\u0639\u0627\u0645\u0629 \u0648\u0627\u0644\u0642\u064a\u0627\u0633\u064a\u0629 \u0644\u0644\u0642\u0637\u0648\u0639 \u0627\u0644\u0632\u0627\u0626\u062f\u0629 \u0645\u0646 \u062a\u0639\u0631\u064a\u0641\u0647\u0627 \u0627\u0644\u0647\u0646\u062f\u0633\u064a.<\/li>\n<li><strong>\u0627\u0644\u062a\u0639\u0631\u0641<\/strong> \u0639\u0644\u0649 \u0627\u0644\u0641\u0631\u0648\u0642\u0627\u062a \u0628\u064a\u0646 \u0627\u0644\u0642\u0637\u0648\u0639 \u0627\u0644\u0646\u0627\u0642\u0635\u0629 \u0648\u0627\u0644\u0642\u0637\u0648\u0639 \u0627\u0644\u0632\u0627\u0626\u062f\u0629 \u0645\u0646 \u062d\u064a\u062b \u0627\u0644\u0645\u0633\u0627\u0641\u0627\u062a \u0627\u0644\u0628\u0624\u0631\u064a\u0629.<\/li>\n<\/ol>\n<p>   <strong>\u062c\u062f\u0648\u0644 \u0627\u0644\u0645\u062d\u062a\u0648\u064a\u0627\u062a<\/strong><br \/>\n<a href=\"#1\">\u0627\u0644\u062a\u0639\u0631\u064a\u0641 \u0627\u0644\u0647\u0646\u062f\u0633\u064a \u0644\u0644\u0642\u0637\u0639 \u0627\u0644\u0632\u0627\u0626\u062f<\/a><br \/>\n<a href=\"#2\">\u0627\u0633\u062a\u0646\u062a\u0627\u062c \u0645\u0639\u0627\u062f\u0644\u0629 \u0627\u0644\u0642\u0637\u0648\u0639 \u0627\u0644\u0632\u0627\u0626\u062f\u0629<\/a><br \/>\n<a href=\"#3\">\u0627\u0644\u0645\u0639\u0627\u062f\u0644\u0629 \u0627\u0644\u0639\u0627\u0645\u0629 \u0644\u0644\u0642\u0637\u0648\u0639 \u0627\u0644\u0632\u0627\u0626\u062f\u0629<\/a><br \/>\n<a href=\"#4\">\u0627\u0644\u0645\u0639\u0627\u062f\u0644\u0629 \u0627\u0644\u0642\u064a\u0627\u0633\u064a\u0629 \u0644\u0644\u0642\u0637\u0648\u0639 \u0627\u0644\u0632\u0627\u0626\u062f\u0629<\/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>\u0627\u0644\u062a\u0639\u0631\u064a\u0641 \u0627\u0644\u0647\u0646\u062f\u0633\u064a \u0644\u0644\u0642\u0637\u0639 \u0627\u0644\u0632\u0627\u0626\u062f<\/h2>\n<p style=\"text-align: justify;\">\u0633\u0628\u0642 \u0623\u0646 \u0642\u0645\u0646\u0627 \u0628\u0645\u0631\u0627\u062c\u0639\u0629 \u0645\u0639\u0627\u062f\u0644\u0629 \u0627\u0644\u0642\u0637\u0648\u0639 \u0627\u0644\u0646\u0627\u0642\u0635\u0629 \u0648\u0627\u0644\u062f\u0648\u0627\u0626\u0631 \u0648\u0627\u0643\u062a\u0634\u0641\u0646\u0627 \u0623\u0646\u0647\u0627 \u062a\u0623\u062e\u0630 \u0627\u0644\u0634\u0643\u0644 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">ax^2 + bx + cy^2 + dy + e = 0<\/span><\/span>\u060c \u062d\u064a\u062b \u0623\u0646 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">a<\/span><\/span> \u0648 <span class=\"katex-eq\" data-katex-display=\"false\">b<\/span> \u0642\u064a\u0645\u062a\u0627\u0646 \u063a\u064a\u0631 \u0635\u0641\u0631\u064a\u062a\u064a\u0646 \u0648\u0644\u0647\u0645\u0627 \u0646\u0641\u0633 \u0627\u0644\u0625\u0634\u0627\u0631\u0629. \u0644\u0642\u062f \u0630\u0643\u0631\u0646\u0627 \u0623\u0646\u0647 \u0625\u0630\u0627 \u0643\u0627\u0646\u062a <span class=\"katex-eq\" data-katex-display=\"false\">a<\/span> \u0648 <span class=\"katex-eq\" data-katex-display=\"false\">b<\/span> \u062a\u062d\u0645\u0644\u0627\u0646 \u0625\u0634\u0627\u0631\u0627\u062a \u0645\u062a\u0639\u0627\u0643\u0633\u0629\u060c \u0641\u0625\u0646\u0646\u0627 \u0628\u062f\u0644\u0627\u064b \u0645\u0646 \u0627\u0644\u0642\u0637\u0639 \u0627\u0644\u0646\u0627\u0642\u0635 \u0646\u062d\u0635\u0644 \u0639\u0644\u0649 \u0642\u0637\u0639 \u0632\u0627\u0626\u062f. \u0644\u0645 \u0646\u0642\u0644 \u0634\u064a\u0626\u064b\u0627 \u0625\u0636\u0627\u0641\u064a\u064b\u0627 \u0639\u0646 \u0647\u0630\u0647 \u0627\u0644\u0645\u0646\u062d\u0646\u064a\u0627\u062a\u060c \u0648\u0644\u0643\u0646 \u0627\u0644\u0622\u0646 \u0633\u0646\u0643\u0645\u0644 \u0647\u0630\u0627 \u0627\u0644\u0646\u0642\u0635. \u0633\u0646\u0639\u0631\u0651\u0641 \u0627\u0644\u0642\u0637\u0639 \u0627\u0644\u0632\u0627\u0626\u062f \u0647\u0646\u062f\u0633\u064a\u064b\u0627\u060c \u0648\u0645\u0646 \u062e\u0644\u0627\u0644 \u0630\u0644\u0643 \u0633\u0646\u0633\u062a\u0646\u062a\u062c \u0627\u0644\u0645\u0639\u0627\u062f\u0644\u0629 \u0627\u0644\u0639\u0627\u0645\u0629 \u0648\u0627\u0644\u0642\u064a\u0627\u0633\u064a\u0629 \u0644\u0644\u0642\u0637\u0648\u0639 \u0627\u0644\u0632\u0627\u0626\u062f\u0629.<\/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>\u0645\u0646 \u0646\u0627\u062d\u064a\u0629\u060c \u064a\u064f\u0639\u0631\u0651\u0641 \u0627\u0644\u0642\u0637\u0639 \u0627\u0644\u0646\u0627\u0642\u0635<\/strong><\/a> \u0639\u0644\u0649 \u0623\u0646\u0647 \u0645\u062c\u0645\u0648\u0639\u0629 \u0643\u0644 \u0627\u0644\u0646\u0642\u0627\u0637 \u0627\u0644\u062a\u064a \u064a\u0643\u0648\u0646 \u0645\u062c\u0645\u0648\u0639 \u0645\u0633\u0627\u0641\u0627\u062a\u0647\u0627 \u0639\u0646 \u0646\u0642\u0637\u062a\u064a\u0646 \u062a\u064f\u0633\u0645\u0651\u064e\u064a\u0627\u0646 \u0627\u0644\u0628\u0624\u0631\u062a\u064a\u0646 \u062b\u0627\u0628\u062a\u064b\u0627. \u0648\u0628\u0627\u0644\u0645\u062b\u0644\u060c \u064a\u064f\u0639\u0631\u0651\u064e\u0641 \u0627\u0644\u0642\u0637\u0639 \u0627\u0644\u0632\u0627\u0626\u062f \u0639\u0644\u0649 \u0623\u0646\u0647 \u0645\u062c\u0645\u0648\u0639\u0629 \u0643\u0644 \u0627\u0644\u0646\u0642\u0627\u0637 \u0627\u0644\u062a\u064a \u064a\u0643\u0648\u0646 \u0627\u0644\u0641\u0631\u0642 \u0627\u0644\u0645\u0637\u0644\u0642 \u0628\u064a\u0646 \u0645\u0633\u0627\u0641\u0627\u062a\u0647\u0627 \u0639\u0646 \u0627\u0644\u0628\u0624\u0631\u062a\u064a\u0646 \u062b\u0627\u0628\u062a\u064b\u0627.<\/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=\"\u0627\u0644\u062a\u0639\u0631\u064a\u0641 \u0627\u0644\u0647\u0646\u062f\u0633\u064a \u0644\u0644\u0642\u0637\u0639 \u0627\u0644\u0632\u0627\u0626\u062f\" 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=\"\u0627\u0644\u062a\u0639\u0631\u064a\u0641 \u0627\u0644\u0647\u0646\u062f\u0633\u064a \u0644\u0644\u0642\u0637\u0639 \u0627\u0644\u0632\u0627\u0626\u062f\" class=\" aligncenter lazyload\" width=\"493\" height=\"340\" \/><\/noscript><\/p>\n<p style=\"text-align: justify;\">\u0628\u0645\u0639\u0646\u0649 \u0622\u062e\u0631\u060c \u062a\u062a\u062d\u0642\u0642 \u0627\u0644\u0639\u0644\u0627\u0642\u0629 \u0627\u0644\u062a\u0627\u0644\u064a\u0629:<\/p>\n<p style=\"text-align: center;\"><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">|d(f_1,P) - d(f_2,P)| = 2a<\/span><\/span><\/p>\n<p style=\"text-align: justify;\">\u062d\u064a\u062b \u0623\u0646 <span class=\"katex-eq\" data-katex-display=\"false\">a<\/span> \u0639\u062f\u062f \u062d\u0642\u064a\u0642\u064a \u062b\u0627\u0628\u062a.<\/p>\n<p style=\"text-align: justify;\">\u064a\u0646\u062a\u062c \u0639\u0646 \u0647\u0630\u0627 \u0641\u0639\u0644\u064a\u064b\u0627 \u0645\u0639\u0627\u062f\u0644\u062a\u064a\u0646: <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">d(f_1,P) - d(f_2,P) = 2a<\/span><\/span> \u0648 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">d(f_2,P) - d(f_1,P) = 2a<\/span><\/span>\u060c \u0625\u062d\u062f\u0627\u0647\u0645\u0627 \u0644\u0643\u0644 \u0641\u0631\u0639 \u0645\u0646 \u0641\u0631\u0648\u0639 \u0627\u0644\u0642\u0637\u0639 \u0627\u0644\u0632\u0627\u0626\u062f.<\/p>\n<p><a name=\"2\"><\/a>  <\/p>\n<h2>\u0627\u0633\u062a\u0646\u062a\u0627\u062c \u0645\u0639\u0627\u062f\u0644\u0629 \u0627\u0644\u0642\u0637\u0648\u0639 \u0627\u0644\u0632\u0627\u0626\u062f\u0629<\/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>\u0645\u0646 \u0627\u0644\u062a\u0639\u0631\u064a\u0641 \u0627\u0644\u0647\u0646\u062f\u0633\u064a\u060c \u064a\u0645\u0643\u0646\u0646\u0627 \u0627\u0644\u062d\u0635\u0648\u0644 \u0639\u0644\u0649<\/strong><\/a> \u0627\u0644\u062a\u0645\u062b\u064a\u0644 \u0627\u0644\u062c\u0628\u0631\u064a \u0644\u0644\u0642\u0637\u0648\u0639 \u0627\u0644\u0632\u0627\u0626\u062f\u0629. \u0633\u0646\u0628\u062f\u0623 \u0645\u0646 \u0627\u0644\u062d\u0627\u0644\u0629 \u0627\u0644\u0623\u0628\u0633\u0637\u060c \u0648\u0645\u0646 \u0647\u0646\u0627\u0643 \u0633\u0646\u0639\u0645\u0645 \u0627\u0644\u0627\u0633\u062a\u0646\u062a\u0627\u062c\u0627\u062a. \u0633\u064a\u0643\u0648\u0646 \u0645\u0646\u0637\u0642\u0646\u0627 \u0645\u0628\u0646\u064a\u064b\u0627 \u0639\u0644\u0649 \u0641\u0631\u0639 \u0648\u0627\u062d\u062f \u0645\u0646 \u0627\u0644\u0642\u0637\u0639 \u0627\u0644\u0632\u0627\u0626\u062f\u060c \u0648\u0627\u0644\u0641\u0631\u0639 \u0627\u0644\u0622\u062e\u0631 \u0633\u064a\u062a\u0645 \u0627\u0644\u062a\u0639\u0627\u0645\u0644 \u0645\u0639\u0647 \u0628\u0646\u0641\u0633 \u0627\u0644\u0645\u0646\u0637\u0642.<\/p>\n<h3>\u0627\u0633\u062a\u0646\u062a\u0627\u062c \u0627\u0644\u0634\u0643\u0644 \u0627\u0644\u0645\u0628\u0633\u0637<\/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>\u0644\u0646\u0639\u062a\u0628\u0631 \u0646\u0642\u0637\u062a\u064a\u0646 \u0628\u0624\u0631\u064a\u062a\u064a\u0646<\/strong><\/a> <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">f_1 = (-c,0)<\/span><\/span> \u0648 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">f_2 = (c,0).<\/span><\/span> \u0627\u0644\u0646\u0642\u0637\u0629 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">p = (x,y)<\/span><\/span> \u0633\u062a\u0643\u0648\u0646 \u0639\u0644\u0649 \u0627\u0644\u0642\u0637\u0639 \u0627\u0644\u0632\u0627\u0626\u062f \u0625\u0630\u0627:<\/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=\"\u0642\u0637\u0639 \u0632\u0627\u0626\u062f \u0645\u062a\u0645\u0631\u0643\u0632 \u0639\u0646\u062f \u0627\u0644\u0623\u0635\u0644\" 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=\"\u0642\u0637\u0639 \u0632\u0627\u0626\u062f \u0645\u062a\u0645\u0631\u0643\u0632 \u0639\u0646\u062f \u0627\u0644\u0623\u0635\u0644\" class=\"aligncenter  lazyload\" width=\"342\" height=\"288\" \/><\/noscript><\/p>\n<p style=\"text-align: center;\"><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\sqrt{(x+c)^2+y^2} - \\sqrt{(x-c)^2+y^2} = 2a<\/span><\/span><\/p>\n<p>   &nbsp;<\/p>\n<p style=\"text-align: justify;\">\u0648\u0645\u0646 \u0647\u0646\u0627 \u064a\u0645\u0643\u0646\u0646\u0627 \u0627\u0644\u062a\u0648\u0635\u0644 \u0625\u0644\u0649 \u0627\u0644\u0645\u0646\u0637\u0642 \u0627\u0644\u062a\u0627\u0644\u064a:<\/p>\n<table style=\"text-align: justify;\">\n<tbody>\n<tr>\n<td><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\sqrt{(x+c)^2+y^2} - \\sqrt{(x-c)^2+y^2} = 2a<\/span><\/span><\/td>\n<td>; \u0645\u0639\u0627\u062f\u0644\u0629 \u0627\u0644\u0642\u0637\u0648\u0639 \u0627\u0644\u0632\u0627\u0626\u062f\u0629<\/td>\n<\/tr>\n<tr><\/tr>\n<tr>\n<td><span dir=\"ltr\"><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><\/span><\/td>\n<td>; \u062a\u0648\u0633\u064a\u0639 \u0627\u0644\u0645\u0631\u0628\u0639\u0627\u062a<\/td>\n<\/tr>\n<tr><\/tr>\n<tr>\n<td><span dir=\"ltr\"><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><\/span><\/td>\n<td>; \u0625\u0639\u0627\u062f\u0629 \u062a\u0648\u0632\u064a\u0639 \u0627\u0644\u062d\u062f\u0648\u062f<\/td>\n<\/tr>\n<tr><\/tr>\n<tr>\n<td><span dir=\"ltr\"><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><\/span><\/td>\n<td>; \u062a\u0631\u0628\u064a\u0639 \u0643\u0644\u0627 \u0627\u0644\u0637\u0631\u0641\u064a\u0646<\/td>\n<\/tr>\n<tr><\/tr>\n<tr>\n<td><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\"> 2xc = 4a^2 + 4a\\sqrt{x^2 - 2xc + c^2 + y^2} - 2xc <\/span><\/span><\/td>\n<td>; \u062d\u0630\u0641 \u0627\u0644\u062d\u062f\u0648\u062f \u0627\u0644\u0645\u062a\u0634\u0627\u0628\u0647\u0629<\/td>\n<\/tr>\n<tr><\/tr>\n<tr>\n<td><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\"> 4xc = 4a^2 + 4a\\sqrt{x^2 - 2xc + c^2 + y^2} <\/span><\/span><\/td>\n<td>; \u0625\u0639\u0627\u062f\u0629 \u062a\u0648\u0632\u064a\u0639 \u0627\u0644\u062d\u062f\u0648\u062f \u0627\u0644\u0645\u062a\u0634\u0627\u0628\u0647\u0629<\/td>\n<\/tr>\n<tr><\/tr>\n<tr>\n<td><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\"> xc = a^2 + a\\sqrt{x^2 - 2xc + c^2 + y^2} <\/span><\/span><\/td>\n<td>; \u062a\u0628\u0633\u064a\u0637 \u0627\u0644\u062d\u062f\u0648\u062f \u0627\u0644\u0645\u062a\u0634\u0627\u0628\u0647\u0629<\/td>\n<\/tr>\n<tr><\/tr>\n<tr>\n<td><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\"> xc - a^2 = a\\sqrt{x^2 - 2xc + c^2 + y^2} <\/span><\/span><\/td>\n<td>; \u062a\u0628\u0633\u064a\u0637 \u0627\u0644\u062d\u062f\u0648\u062f \u0627\u0644\u0645\u062a\u0634\u0627\u0628\u0647\u0629<\/td>\n<\/tr>\n<tr><\/tr>\n<tr>\n<td><span dir=\"ltr\"><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><\/span><\/td>\n<td>; \u062a\u0631\u0628\u064a\u0639 \u0643\u0644\u0627 \u0627\u0644\u0637\u0631\u0641\u064a\u0646<\/td>\n<\/tr>\n<tr><\/tr>\n<tr>\n<td><span dir=\"ltr\"><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><\/span><\/td>\n<td>; \u062a\u0648\u0633\u064a\u0639 \u0627\u0644\u0623\u0642\u0648\u0627\u0633<\/td>\n<\/tr>\n<tr><\/tr>\n<tr>\n<td><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\"> x^2c^2 + a^4 = a^2x^2 + a^2c^2 + a^2y^2 <\/span><\/span><\/td>\n<td>; \u062d\u0630\u0641 \u0627\u0644\u062d\u062f\u0648\u062f \u0627\u0644\u0645\u062a\u0634\u0627\u0628\u0647\u0629<\/td>\n<\/tr>\n<tr><\/tr>\n<tr>\n<td><span dir=\"ltr\"><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><\/span><\/td>\n<td>; \u0625\u0639\u0627\u062f\u0629 \u062a\u0631\u062a\u064a\u0628 \u0627\u0644\u062d\u062f\u0648\u062f<\/td>\n<\/tr>\n<tr><\/tr>\n<tr>\n<td><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle \\frac{x^2}{a^2} - \\frac{y^2}{c^2 - a^2} = 1 <\/span><\/span><\/td>\n<td>; \u0625\u0639\u0627\u062f\u0629 \u062a\u0631\u062a\u064a\u0628 \u0627\u0644\u062d\u062f\u0648\u062f<\/td>\n<\/tr>\n<tr><\/tr>\n<\/tbody>\n<\/table>\n<p style=\"text-align: justify;\">\u0644\u0644\u062a\u0639\u0628\u064a\u0631 \u0627\u0644\u0623\u062e\u064a\u0631 \u0647\u0630\u0627\u060c \u0643\u0645\u0627 \u0647\u0648 \u0627\u0644\u062d\u0627\u0644 \u0645\u0639 \u0627\u0644\u0642\u0637\u0648\u0639 \u0627\u0644\u0646\u0627\u0642\u0635\u0629\u060c \u0646\u0623\u062e\u0630 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">b^2=c^2-a^2<\/span><\/span> \u0648\u0646\u0635\u0644 \u0625\u0644\u0649 \u0645\u0639\u0627\u062f\u0644\u0629 \u0627\u0644\u0642\u0637\u0648\u0639 \u0627\u0644\u0632\u0627\u0626\u062f\u0629:<\/p>\n<p style=\"text-align: center;\"><span dir=\"ltr\"><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><\/span><\/p>\n<p><a name=\"3\"><\/a>     <\/p>\n<h2>\u0627\u0644\u0645\u0639\u0627\u062f\u0644\u0629 \u0627\u0644\u0639\u0627\u0645\u0629 \u0644\u0644\u0642\u0637\u0648\u0639 \u0627\u0644\u0632\u0627\u0626\u062f\u0629<\/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>\u0644\u0627\u0633\u062a\u0646\u062a\u0627\u062c \u0627\u0644\u0645\u0639\u0627\u062f\u0644\u0629 \u0627\u0644\u0639\u0627\u0645\u0629<\/strong><\/a> \u0644\u0644\u0642\u0637\u0648\u0639 \u0627\u0644\u0632\u0627\u0626\u062f\u0629\u060c \u064a\u0643\u0641\u064a \u0623\u0646 \u0646\u0623\u062e\u0630 \u0627\u0644\u0645\u0639\u0627\u062f\u0644\u0629 \u0627\u0644\u062a\u064a \u0627\u0633\u062a\u0646\u062a\u062c\u0646\u0627\u0647\u0627 \u0644\u0644\u062a\u0648 \u0648\u0646\u0637\u0628\u0642 \u062a\u062d\u0648\u064a\u0644\u0627\u062a \u0627\u0644\u0645\u0648\u0642\u0639:<\/p>\n<table style=\"text-align: justify;\">\n<tbody>\n<tr>\n<td><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">x\\longmapsto x-h<\/span><\/span><\/td>\n<\/tr>\n<tr>\n<td><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">y\\longmapsto y-k<\/span><\/span><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p style=\"text-align: justify;\">\u0648\u0628\u0630\u0644\u0643 \u0646\u062d\u0635\u0644 \u062a\u0644\u0642\u0627\u0626\u064a\u064b\u0627 \u0639\u0644\u0649 \u0627\u0644\u0645\u0639\u0627\u062f\u0644\u0629 \u0627\u0644\u0639\u0627\u0645\u0629 \u0644\u0644\u0642\u0637\u0639 \u0627\u0644\u0632\u0627\u0626\u062f \u0645\u0639 \u0645\u0631\u0643\u0632 \u0641\u064a <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">(h,k)<\/span><\/span><\/p>\n<p style=\"text-align: center;\"><span dir=\"ltr\"><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><\/span><\/p>\n<p><a name=\"4\"><\/a>     <\/p>\n<h2>\u0627\u0644\u0645\u0639\u0627\u062f\u0644\u0629 \u0627\u0644\u0642\u064a\u0627\u0633\u064a\u0629 \u0644\u0644\u0642\u0637\u0648\u0639 \u0627\u0644\u0632\u0627\u0626\u062f\u0629<\/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>\u0648\u0627\u0644\u0622\u0646 \u0625\u0630\u0627 \u0623\u062e\u0630\u0646\u0627 \u0627\u0644\u0645\u0639\u0627\u062f\u0644\u0629 \u0627\u0644\u0639\u0627\u0645\u0629<\/strong><\/a> \u0644\u0644\u0642\u0637\u0648\u0639 \u0627\u0644\u0632\u0627\u0626\u062f\u0629 \u0648\u0642\u0645\u0646\u0627 \u0628\u062a\u0648\u0633\u064a\u0639\u0647\u0627\u060c \u0633\u0646\u0635\u0644 \u0625\u0644\u0649 \u0627\u0644\u062a\u0639\u0628\u064a\u0631 \u0627\u0644\u0642\u064a\u0627\u0633\u064a:<\/p>\n<table style=\"text-align: justify;\">\n<tbody>\n<tr>\n<td><span dir=\"ltr\"><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><\/span><\/td>\n<td>; \u0627\u0644\u0645\u0639\u0627\u062f\u0644\u0629 \u0627\u0644\u0639\u0627\u0645\u0629 \u0644\u0644\u0642\u0637\u0648\u0639 \u0627\u0644\u0632\u0627\u0626\u062f\u0629<\/td>\n<\/tr>\n<tr>\n<td><span dir=\"ltr\"><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><\/span><\/td>\n<td>; \u062a\u0648\u0633\u064a\u0639 \u0627\u0644\u0645\u0631\u0628\u0639\u0627\u062a \u0648\u0636\u0631\u0628 \u062c\u0645\u064a\u0639 \u0627\u0644\u062d\u062f\u0648\u062f \u0641\u064a <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">a^2b^2<\/span><\/span><\/td>\n<\/tr>\n<tr>\n<td><span dir=\"ltr\"><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><\/span><\/td>\n<td>; \u062a\u0648\u0633\u064a\u0639 \u0627\u0644\u0623\u0642\u0648\u0627\u0633<\/td>\n<\/tr>\n<tr>\n<td><span dir=\"ltr\"><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><\/span><\/td>\n<td>; \u062a\u062c\u0645\u064a\u0639 \u0627\u0644\u062d\u062f\u0648\u062f \u0627\u0644\u0645\u062a\u0634\u0627\u0628\u0647\u0629<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p style=\"text-align: justify;\">\u0647\u0630\u0627 \u0627\u0644\u062a\u0639\u0628\u064a\u0631 \u0627\u0644\u0623\u062e\u064a\u0631 \u0644\u0647 \u0627\u0644\u0634\u0643\u0644 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">Ax^2+Bx + Cy^2 + Dy + E = 0,<\/span><\/span> \u062d\u064a\u062b \u0623\u0646 <span class=\"katex-eq\" data-katex-display=\"false\">A<\/span> \u0648 <span class=\"katex-eq\" data-katex-display=\"false\">C<\/span> \u062f\u0627\u0626\u0645\u064b\u0627 \u063a\u064a\u0631 \u0635\u0641\u0631\u064a\u064a\u0646 \u0648\u0644\u0647\u0645\u0627 \u0625\u0634\u0627\u0631\u0627\u062a \u0645\u062a\u0639\u0627\u0643\u0633\u0629\u060c \u0643\u0645\u0627 \u0633\u0628\u0642 \u0623\u0646 \u0623\u0634\u0631\u0646\u0627 \u0639\u0646\u062f\u0645\u0627 \u062f\u0631\u0633\u0646\u0627 \u0627\u0644\u0642\u0637\u0648\u0639 \u0627\u0644\u0646\u0627\u0642\u0635\u0629.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>\u0645\u0639\u0627\u062f\u0644\u0629 \u0627\u0644\u0642\u0637\u0648\u0639 \u0627\u0644\u0632\u0627\u0626\u062f\u0629 \u0648\u0627\u0633\u062a\u0646\u062a\u0627\u062c\u0647\u0627 \u0627\u0644\u0645\u0644\u062e\u0635: \u0641\u064a \u0647\u0630\u0627 \u0627\u0644\u062f\u0631\u0633\u060c \u0633\u0646\u0633\u062a\u0643\u0634\u0641 \u0627\u0644\u062a\u0639\u0631\u064a\u0641 \u0627\u0644\u0647\u0646\u062f\u0633\u064a \u0644\u0644\u0642\u0637\u0639 \u0627\u0644\u0632\u0627\u0626\u062f\u060c \u0648\u0646\u0642\u0627\u0631\u0646\u0647 \u0628\u0627\u0644\u0642\u0637\u0639 \u0627\u0644\u0646\u0627\u0642\u0635\u060c \u0648\u0633\u0646\u0633\u062a\u0646\u062a\u062c \u0645\u0639\u0627\u062f\u0644\u062a\u0647 \u0627\u0644\u0639\u0627\u0645\u0629 \u0648\u0627\u0644\u0642\u064a\u0627\u0633\u064a\u0629. \u0623\u0647\u062f\u0627\u0641 \u0627\u0644\u062a\u0639\u0644\u0645: \u0641\u064a \u0646\u0647\u0627\u064a\u0629 \u0647\u0630\u0627 \u0627\u0644\u062f\u0631\u0633\u060c \u0633\u064a\u0643\u0648\u0646 \u0627\u0644\u0637\u0627\u0644\u0628 \u0642\u0627\u062f\u0631\u064b\u0627 \u0639\u0644\u0649: 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