{"id":30620,"date":"2023-09-18T09:55:41","date_gmt":"2023-09-18T02:55:41","guid":{"rendered":"https:\/\/ungdung.hotronghiencuu.com\/open\/tiep-tuyen-la-gi"},"modified":"2023-09-18T09:55:41","modified_gmt":"2023-09-18T02:55:41","slug":"tiep-tuyen-la-gi","status":"publish","type":"post","link":"https:\/\/ungdung.hotronghiencuu.com\/open\/tiep-tuyen-la-gi","title":{"rendered":"Ti\u1ebfp tuy\u1ebfn: \u0110\u1ecbnh ngh\u0129a, t\u00ednh ch\u1ea5t v\u00e0 d\u1ea5u hi\u1ec7u nh\u1eadn bi\u1ebft ti\u1ebfp tuy\u1ebfn \u0111\u01b0\u1eddng tr\u00f2n"},"content":{"rendered":"<p>Ti\u1ebfp tuy\u1ebfn l\u00e0 m\u1ed9t kh\u00e1i ni\u1ec7m trong to\u00e1n h\u1ecdc v\u00e0 v\u1eadt l\u00fd, \u00e1m ch\u1ec9 \u0111\u01b0\u1eddng th\u1eb3ng ti\u1ebfp x\u00fac v\u1edbi m\u1ed9t \u0111\u1ed3 th\u1ecb hay \u0111\u01b0\u1eddng cong t\u1ea1i m\u1ed9t \u0111i\u1ec3m c\u1ee5 th\u1ec3. Kh\u00e1i ni\u1ec7m n\u00e0y c\u00f3 \u1ee9ng d\u1ee5ng r\u1ed9ng r\u00e3i trong c\u00e1c l\u0129nh v\u1ef1c nh\u01b0 t\u00edch ph\u00e2n, \u0111\u1ea1o h\u00e0m v\u00e0 t\u1ef7 l\u1ec7 thay \u0111\u1ed5i. Vi\u1ec7c hi\u1ec3u r\u00f5 v\u1ec1 ti\u1ebfp tuy\u1ebfn gi\u00fap ch\u00fang ta n\u1eafm b\u1eaft \u0111\u01b0\u1ee3c s\u1ef1 bi\u1ebfn thi\u00ean c\u1ee7a c\u00e1c h\u00e0m s\u1ed1 v\u00e0 hi\u1ec7u qu\u1ea3 trong vi\u1ec7c gi\u1ea3i quy\u1ebft c\u00e1c b\u00e0i to\u00e1n ph\u1ee9c t\u1ea1p.<\/p>\n<div id=\"ez-toc-container\" class=\"ez-toc-v2_0_40 counter-hierarchy ez-toc-counter ez-toc-grey ez-toc-container-direction\">\n<div class=\"ez-toc-title-container\">\n<p class=\"ez-toc-title\">Table of Contents<\/p>\n<span class=\"ez-toc-title-toggle\"><a href=\"#\" class=\"ez-toc-pull-right ez-toc-btn ez-toc-btn-xs ez-toc-btn-default ez-toc-toggle\" area-label=\"ez-toc-toggle-icon-1\"><label for=\"item-6acdc93b016d9\" aria-label=\"Table of Content\"><span style=\"display: flex;align-items: center;width: 35px;height: 30px;justify-content: center;direction:ltr;\"><svg style=\"fill: #999;color:#999\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" class=\"list-377408\" width=\"20px\" height=\"20px\" viewBox=\"0 0 24 24\" fill=\"none\"><path d=\"M6 6H4v2h2V6zm14 0H8v2h12V6zM4 11h2v2H4v-2zm16 0H8v2h12v-2zM4 16h2v2H4v-2zm16 0H8v2h12v-2z\" fill=\"currentColor\"><\/path><\/svg><svg style=\"fill: #999;color:#999\" class=\"arrow-unsorted-368013\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"10px\" height=\"10px\" viewBox=\"0 0 24 24\" version=\"1.2\" baseProfile=\"tiny\"><path d=\"M18.2 9.3l-6.2-6.3-6.2 6.3c-.2.2-.3.4-.3.7s.1.5.3.7c.2.2.4.3.7.3h11c.3 0 .5-.1.7-.3.2-.2.3-.5.3-.7s-.1-.5-.3-.7zM5.8 14.7l6.2 6.3 6.2-6.3c.2-.2.3-.5.3-.7s-.1-.5-.3-.7c-.2-.2-.4-.3-.7-.3h-11c-.3 0-.5.1-.7.3-.2.2-.3.5-.3.7s.1.5.3.7z\"\/><\/svg><\/span><\/label><input  type=\"checkbox\" id=\"item-6acdc93b016d9\"><\/a><\/span><\/div>\n<nav><ul class='ez-toc-list ez-toc-list-level-1 ' ><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-1\" href=\"https:\/\/ungdung.hotronghiencuu.com\/open\/tiep-tuyen-la-gi\/#1_Tiep_tuyen_la_gi\" title=\"1. Ti\u1ebfp tuy\u1ebfn l\u00e0 g\u00ec?\">1. Ti\u1ebfp tuy\u1ebfn l\u00e0 g\u00ec?<\/a><ul class='ez-toc-list-level-3'><li class='ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-2\" href=\"https:\/\/ungdung.hotronghiencuu.com\/open\/tiep-tuyen-la-gi\/#Vi_du\" title=\"V\u00ed d\u1ee5:\">V\u00ed d\u1ee5:<\/a><ul class='ez-toc-list-level-4'><li class='ez-toc-heading-level-4'><a class=\"ez-toc-link ez-toc-heading-3\" href=\"https:\/\/ungdung.hotronghiencuu.com\/open\/tiep-tuyen-la-gi\/#Tinh_chat\" title=\"T\u00ednh ch\u1ea5t:\">T\u00ednh ch\u1ea5t:<\/a><\/li><\/ul><\/li><\/ul><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-4\" href=\"https:\/\/ungdung.hotronghiencuu.com\/open\/tiep-tuyen-la-gi\/#2_Dinh_nghia_va_tinh_chat_cua_tiep_tuyen_duong_tron\" title=\"2. \u0110\u1ecbnh ngh\u0129a v\u00e0 t\u00ednh ch\u1ea5t c\u1ee7a ti\u1ebfp tuy\u1ebfn \u0111\u01b0\u1eddng tr\u00f2n.\">2. \u0110\u1ecbnh ngh\u0129a v\u00e0 t\u00ednh ch\u1ea5t c\u1ee7a ti\u1ebfp tuy\u1ebfn \u0111\u01b0\u1eddng tr\u00f2n.<\/a><ul class='ez-toc-list-level-3'><li class='ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-5\" href=\"https:\/\/ungdung.hotronghiencuu.com\/open\/tiep-tuyen-la-gi\/#Tinh_chat-2\" title=\"T\u00ednh ch\u1ea5t:\">T\u00ednh ch\u1ea5t:<\/a><\/li><\/ul><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-6\" href=\"https:\/\/ungdung.hotronghiencuu.com\/open\/tiep-tuyen-la-gi\/#3_Dau_hieu_nhan_biet_tiep_tuyen_cua_duong_tron\" title=\"3. D\u1ea5u hi\u1ec7u nh\u1eadn bi\u1ebft ti\u1ebfp tuy\u1ebfn c\u1ee7a \u0111\u01b0\u1eddng tr\u00f2n.\">3. D\u1ea5u hi\u1ec7u nh\u1eadn bi\u1ebft ti\u1ebfp tuy\u1ebfn c\u1ee7a \u0111\u01b0\u1eddng tr\u00f2n.<\/a><ul class='ez-toc-list-level-3'><li class='ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-7\" href=\"https:\/\/ungdung.hotronghiencuu.com\/open\/tiep-tuyen-la-gi\/#31_Diem_tiep_tuyen\" title=\"3.1 \u0110i\u1ec3m ti\u1ebfp tuy\u1ebfn\">3.1 \u0110i\u1ec3m ti\u1ebfp tuy\u1ebfn<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-8\" href=\"https:\/\/ungdung.hotronghiencuu.com\/open\/tiep-tuyen-la-gi\/#32_Giao_diem_hai_duong_tron\" title=\"3.2 Giao \u0111i\u1ec3m hai \u0111\u01b0\u1eddng tr\u00f2n\">3.2 Giao \u0111i\u1ec3m hai \u0111\u01b0\u1eddng tr\u00f2n<\/a><ul class='ez-toc-list-level-4'><li class='ez-toc-heading-level-4'><a class=\"ez-toc-link ez-toc-heading-9\" href=\"https:\/\/ungdung.hotronghiencuu.com\/open\/tiep-tuyen-la-gi\/#Vi_du-2\" title=\"V\u00ed d\u1ee5:\">V\u00ed d\u1ee5:<\/a><\/li><\/ul><\/li><\/ul><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-10\" href=\"https:\/\/ungdung.hotronghiencuu.com\/open\/tiep-tuyen-la-gi\/#4_Cong_thuc_tinh_chu_vi_hinh_chu_nhat_va_ung_dung_cua_tiep_tuyen_trong_kinh_te\" title=\"4. C\u00f4ng th\u1ee9c t\u00ednh chu vi h\u00ecnh ch\u1eef nh\u1eadt v\u00e0 \u1ee9ng d\u1ee5ng c\u1ee7a ti\u1ebfp tuy\u1ebfn trong kinh t\u1ebf.\">4. C\u00f4ng th\u1ee9c t\u00ednh chu vi h\u00ecnh ch\u1eef nh\u1eadt v\u00e0 \u1ee9ng d\u1ee5ng c\u1ee7a ti\u1ebfp tuy\u1ebfn trong kinh t\u1ebf.<\/a><ul class='ez-toc-list-level-3'><li class='ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-11\" href=\"https:\/\/ungdung.hotronghiencuu.com\/open\/tiep-tuyen-la-gi\/#41_Cong_thuc_tinh_chu_vi_hinh_chu_nhat\" title=\"4.1 C\u00f4ng th\u1ee9c t\u00ednh chu vi h\u00ecnh ch\u1eef nh\u1eadt\">4.1 C\u00f4ng th\u1ee9c t\u00ednh chu vi h\u00ecnh ch\u1eef nh\u1eadt<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-12\" href=\"https:\/\/ungdung.hotronghiencuu.com\/open\/tiep-tuyen-la-gi\/#42_Ung_dung_cua_tiep_tuyen_trong_kinh_te\" title=\"4.2 \u1ee8ng d\u1ee5ng c\u1ee7a ti\u1ebfp tuy\u1ebfn trong kinh t\u1ebf\">4.2 \u1ee8ng d\u1ee5ng c\u1ee7a ti\u1ebfp tuy\u1ebfn trong kinh t\u1ebf<\/a><\/li><\/ul><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-13\" href=\"https:\/\/ungdung.hotronghiencuu.com\/open\/tiep-tuyen-la-gi\/#5_Tinh_chat_tiep_tuyen_cua_duong_tron_va_cac_tinh_chat_lien_quan\" title=\"5. T\u00ednh ch\u1ea5t ti\u1ebfp tuy\u1ebfn c\u1ee7a \u0111\u01b0\u1eddng tr\u00f2n v\u00e0 c\u00e1c t\u00ednh ch\u1ea5t li\u00ean quan.\">5. T\u00ednh ch\u1ea5t ti\u1ebfp tuy\u1ebfn c\u1ee7a \u0111\u01b0\u1eddng tr\u00f2n v\u00e0 c\u00e1c t\u00ednh ch\u1ea5t li\u00ean quan.<\/a><ul class='ez-toc-list-level-3'><li class='ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-14\" href=\"https:\/\/ungdung.hotronghiencuu.com\/open\/tiep-tuyen-la-gi\/#Tinh_chat_tiep_tuyen\" title=\"T\u00ednh ch\u1ea5t ti\u1ebfp tuy\u1ebfn:\">T\u00ednh ch\u1ea5t ti\u1ebfp tuy\u1ebfn:<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-15\" href=\"https:\/\/ungdung.hotronghiencuu.com\/open\/tiep-tuyen-la-gi\/#Tinh_chat_lien_quan\" title=\"T\u00ednh ch\u1ea5t li\u00ean quan:\">T\u00ednh ch\u1ea5t li\u00ean quan:<\/a><\/li><\/ul><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-16\" href=\"https:\/\/ungdung.hotronghiencuu.com\/open\/tiep-tuyen-la-gi\/#6_Cach_xac_dinh_goc_giua_hai_tiep_tuyen_va_cac_tinh_chat_lien_quan\" title=\"6. C\u00e1ch x\u00e1c \u0111\u1ecbnh g\u00f3c gi\u1eefa hai ti\u1ebfp tuy\u1ebfn v\u00e0 c\u00e1c t\u00ednh ch\u1ea5t li\u00ean quan.\">6. C\u00e1ch x\u00e1c \u0111\u1ecbnh g\u00f3c gi\u1eefa hai ti\u1ebfp tuy\u1ebfn v\u00e0 c\u00e1c t\u00ednh ch\u1ea5t li\u00ean quan.<\/a><ul class='ez-toc-list-level-3'><li class='ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-17\" href=\"https:\/\/ungdung.hotronghiencuu.com\/open\/tiep-tuyen-la-gi\/#Xac_dinh_goc_giua_hai_tiep_tuyen\" title=\"X\u00e1c \u0111\u1ecbnh g\u00f3c gi\u1eefa hai ti\u1ebfp tuy\u1ebfn:\">X\u00e1c \u0111\u1ecbnh g\u00f3c gi\u1eefa hai ti\u1ebfp tuy\u1ebfn:<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-18\" href=\"https:\/\/ungdung.hotronghiencuu.com\/open\/tiep-tuyen-la-gi\/#Tinh_chat_lien_quan-2\" title=\"T\u00ednh ch\u1ea5t li\u00ean quan:\">T\u00ednh ch\u1ea5t li\u00ean quan:<\/a><\/li><\/ul><\/li><\/ul><\/nav><\/div>\n<h2><span class=\"ez-toc-section\" id=\"1_Tiep_tuyen_la_gi\"><\/span>1. Ti\u1ebfp tuy\u1ebfn l\u00e0 g\u00ec?<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p><img decoding=\"async\" alt=\"1. Ti\u1ebfp tuy\u1ebfn l\u00e0 g\u00ec?\" src=\"https:\/\/ungdung.hotronghiencuu.com\/open\/wp-content\/uploads\/2023\/09\/tiep_tuyen_dinh_nghia_tinh_chat_va_dau_hieu_nhan_biet_tiep_tuyen_duong_tron.jpg\" style=\"text-align: center; clear: both; display: block; margin: 0 auto;\" title=\"1. Ti\u1ebfp tuy\u1ebfn l\u00e0 g\u00ec?\"\/><\/p>\n<p>Trong h\u00ecnh h\u1ecdc, ti\u1ebfp tuy\u1ebfn l\u00e0 m\u1ed9t \u0111\u01b0\u1eddng th\u1eb3ng ch\u1ec9 c\u1eaft m\u1ed9t \u0111\u01b0\u1eddng cong t\u1ea1i m\u1ed9t \u0111i\u1ec3m duy nh\u1ea5t v\u00e0 c\u00f3 c\u00f9ng h\u01b0\u1edbng v\u1edbi \u0111\u01b0\u1eddng cong t\u1ea1i \u0111i\u1ec3m \u0111\u00f3. \u0110i\u1ec3m ti\u1ebfp tuy\u1ebfn l\u00e0 \u0111i\u1ec3m giao nhau c\u1ee7a ti\u1ebfp tuy\u1ebfn v\u00e0 \u0111\u01b0\u1eddng cong.<\/p>\n<h3><span class=\"ez-toc-section\" id=\"Vi_du\"><\/span>V\u00ed d\u1ee5:<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p>X\u00e9t tr\u01b0\u1eddng h\u1ee3p c\u1ee7a m\u1ed9t \u0111\u01b0\u1eddng tr\u00f2n. M\u1ed7i \u0111i\u1ec3m tr\u00ean \u0111\u01b0\u1eddng tr\u00f2n c\u00f3 th\u1ec3 c\u00f3 m\u1ed9t ti\u1ebfp tuy\u1ebfn duy nh\u1ea5t. Ti\u1ebfp tuy\u1ebfn n\u00e0y s\u1ebd c\u1eaft \u0111\u01b0\u1eddng tr\u00f2n t\u1ea1i \u0111i\u1ec3m \u0111\u00f3 v\u00e0 c\u00f3 c\u00f9ng h\u01b0\u1edbng v\u1edbi \u0111\u01b0\u1eddng tr\u00f2n t\u1ea1i \u0111i\u1ec3m \u0111\u00f3.<\/p>\n<h4><span class=\"ez-toc-section\" id=\"Tinh_chat\"><\/span>T\u00ednh ch\u1ea5t:<span class=\"ez-toc-section-end\"><\/span><\/h4>\n<ul>\n<li>M\u1ed9t ti\u1ebfp tuy\u1ebfn kh\u00f4ng bao gi\u1edd c\u1eaft ho\u1eb7c ch\u1ea1m qua b\u00ean trong c\u1ee7a \u0111\u01b0\u1eddng cong.<\/li>\n<li>M\u1ed9t ti\u1ebfp tuy\u1ebfn ch\u1ec9 c\u1eaft ho\u1eb7c ch\u1ea1m qua b\u00ean ngo\u00e0i c\u1ee7a \u0111\u01b0\u1eddng cong.<\/li>\n<li>\u0110\u1ed9 d\u1ed1c c\u1ee7a ti\u1ebfp tuy\u1ebfn l\u00e0 b\u1eb1ng v\u1edbi \u0111\u1ed9 d\u1ed1c c\u1ee7a \u0111\u01b0\u1eddng cong tai \u0111i\u1ec3m ti\u1ebfp x\u00fac.<\/li>\n<\/ul>\n<h2><span class=\"ez-toc-section\" id=\"2_Dinh_nghia_va_tinh_chat_cua_tiep_tuyen_duong_tron\"><\/span>2. \u0110\u1ecbnh ngh\u0129a v\u00e0 t\u00ednh ch\u1ea5t c\u1ee7a ti\u1ebfp tuy\u1ebfn \u0111\u01b0\u1eddng tr\u00f2n.<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>\u0110\u1ed1i v\u1edbi m\u1ed9t \u0111\u01b0\u1eddng tr\u00f2n, ti\u1ebfp tuy\u1ebfn l\u00e0 m\u1ed9t \u0111\u01b0\u1eddng th\u1eb3ng ch\u1ec9 c\u1eaft \u0111\u01b0\u1eddng tr\u00f2n t\u1ea1i m\u1ed9t \u0111i\u1ec3m duy nh\u1ea5t v\u00e0 c\u00f3 c\u00f9ng h\u01b0\u1edbng v\u1edbi \u0111\u01b0\u1eddng tr\u00f2n t\u1ea1i \u0111i\u1ec3m \u0111\u00f3. \u0110i\u1ec3m ti\u1ebfp tuy\u1ebfn l\u00e0 \u0111i\u1ec3m giao nhau c\u1ee7a ti\u1ebfp tuy\u1ebfn v\u00e0 \u0111\u01b0\u1eddng tr\u00f2n.<\/p>\n<h3><span class=\"ez-toc-section\" id=\"Tinh_chat-2\"><\/span>T\u00ednh ch\u1ea5t:<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<ul>\n<li>M\u1ed9t ti\u1ebfp tuy\u1ebfn c\u1ee7a \u0111\u01b0\u1eddng tr\u00f2n lu\u00f4n vu\u00f4ng g\u00f3c v\u1edbi b\u00e1n k\u00ednh \u0111i qua \u0111i\u1ec3m ti\u1ebfp x\u00fac.<\/li>\n<li>\u0110\u1ed9 d\u1ed1c c\u1ee7a ti\u1ebfp tuy\u1ebfn l\u00e0 b\u1eb1ng v\u1edbi \u0111\u1ed9 d\u1ed1c c\u1ee7a b\u00e1n k\u00ednh \u0111i qua \u0111i\u1ec3m ti\u1ebfp x\u00fac.<\/li>\n<li>N\u1ebfu hai \u0111\u01b0\u1eddng tr\u00f2n c\u00f3 m\u1ed9t ti\u1ebfp tuy\u1ebfn chung, th\u00ec c\u00e1c b\u00e1n k\u00ednh c\u1ee7a hai \u0111\u01b0\u1eddng tr\u00f2n s\u1ebd song song v\u1edbi nhau.<\/li>\n<\/ul>\n<h2><span class=\"ez-toc-section\" id=\"3_Dau_hieu_nhan_biet_tiep_tuyen_cua_duong_tron\"><\/span>3. D\u1ea5u hi\u1ec7u nh\u1eadn bi\u1ebft ti\u1ebfp tuy\u1ebfn c\u1ee7a \u0111\u01b0\u1eddng tr\u00f2n.<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<h3><span class=\"ez-toc-section\" id=\"31_Diem_tiep_tuyen\"><\/span>3.1 \u0110i\u1ec3m ti\u1ebfp tuy\u1ebfn<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p>\u0110\u1ec3 x\u00e1c \u0111\u1ecbnh m\u1ed9t \u0111i\u1ec3m P c\u00f3 thu\u1ed9c ti\u1ebfp tuy\u1ebfn c\u1ee7a \u0111\u01b0\u1eddng tr\u00f2n (O), ta c\u1ea7n ki\u1ec3m tra xem \u0111o\u1ea1n th\u1eb3ng OP c\u00f3 vu\u00f4ng g\u00f3c v\u1edbi b\u00e1n k\u00ednh c\u1ee7a \u0111\u01b0\u1eddng tr\u00f2n hay kh\u00f4ng. N\u1ebfu OP vu\u00f4ng g\u00f3c v\u1edbi b\u00e1n k\u00ednh, t\u1ee9c l\u00e0 OP l\u00e0 ti\u1ebfp tuy\u1ebfn c\u1ee7a \u0111\u01b0\u1eddng tr\u00f2n.<\/p>\n<h3><span class=\"ez-toc-section\" id=\"32_Giao_diem_hai_duong_tron\"><\/span>3.2 Giao \u0111i\u1ec3m hai \u0111\u01b0\u1eddng tr\u00f2n<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p>N\u1ebfu hai \u0111\u01b0\u1eddng tr\u00f2n (O1) v\u00e0 (O2) c\u00f3 giao \u0111i\u1ec3m duy nh\u1ea5t l\u00e0 m\u1ed9t \u0111i\u1ec3m P, th\u00ec \u0111o\u1ea1n th\u1eb3ng n\u1ed1i hai t\u00e2m O1 v\u00e0 O2 s\u1ebd l\u00e0 ti\u1ebfp tuy\u1ebfn chung c\u1ee7a hai \u0111\u01b0\u1eddng tr\u00f2n.<\/p>\n<h4><span class=\"ez-toc-section\" id=\"Vi_du-2\"><\/span>V\u00ed d\u1ee5:<span class=\"ez-toc-section-end\"><\/span><\/h4>\n<p>Cho hai \u0111\u01b0\u1eddng tr\u00f2n (O1) v\u00e0 (O2) c\u00f3 c\u00e1c ph\u01b0\u01a1ng tr\u00ecnh:<br \/>\n(O1): x^2 + y^2 &#8211; 6x + 8y &#8211; 7 = 0<br \/>\n(O2): x^2 + y^2 &#8211; 10x + 12y &#8211; 21 = 0<\/p>\n<p>\u0110\u1ec3 t\u00ecm ti\u1ebfp tuy\u1ebfn chung c\u1ee7a hai \u0111\u01b0\u1eddng tr\u00f2n n\u00e0y, ta c\u1ea7n gi\u1ea3i h\u1ec7 ph\u01b0\u01a1ng tr\u00ecnh:<br \/>\n{<br \/>\n    x^2 + y^2 &#8211; 6x + 8y &#8211; 7 = 0<br \/>\n    x^2 + y^2 &#8211; 10x + 12y &#8211; 21 = 0<br \/>\n}<\/p>\n<p>Sau khi gi\u1ea3i h\u1ec7 ph\u01b0\u01a1ng tr\u00ecnh, ta t\u00ecm \u0111\u01b0\u1ee3c giao \u0111i\u1ec3m duy nh\u1ea5t l\u00e0 \u0111i\u1ec3m P(3, -1). V\u1eady \u0111o\u1ea1n th\u1eb3ng n\u1ed1i hai t\u00e2m O1 v\u00e0 O2 l\u00e0 ti\u1ebfp tuy\u1ebfn chung c\u1ee7a hai \u0111\u01b0\u1eddng tr\u00f2n.<\/p>\n<h2><span class=\"ez-toc-section\" id=\"4_Cong_thuc_tinh_chu_vi_hinh_chu_nhat_va_ung_dung_cua_tiep_tuyen_trong_kinh_te\"><\/span>4. C\u00f4ng th\u1ee9c t\u00ednh chu vi h\u00ecnh ch\u1eef nh\u1eadt v\u00e0 \u1ee9ng d\u1ee5ng c\u1ee7a ti\u1ebfp tuy\u1ebfn trong kinh t\u1ebf.<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<h3><span class=\"ez-toc-section\" id=\"41_Cong_thuc_tinh_chu_vi_hinh_chu_nhat\"><\/span>4.1 C\u00f4ng th\u1ee9c t\u00ednh chu vi h\u00ecnh ch\u1eef nh\u1eadt<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p>Chu vi (P) c\u1ee7a m\u1ed9t h\u00ecnh ch\u1eef nh\u1eadt c\u00f3 chi\u1ec1u d\u00e0i (a) v\u00e0 chi\u1ec1u r\u1ed9ng (b) \u0111\u01b0\u1ee3c t\u00ednh b\u1eb1ng c\u00f4ng th\u1ee9c: P = 2(a + b).<\/p>\n<p>V\u00ed d\u1ee5:<br \/>\nCho m\u1ed9t h\u00ecnh ch\u1eef nh\u1eadt c\u00f3 chi\u1ec1u d\u00e0i a = 5 cm v\u00e0 chi\u1ec1u r\u1ed9ng b = 3 cm. \u00c1p d\u1ee5ng c\u00f4ng th\u1ee9c t\u00ednh chu vi, ta c\u00f3: P = 2(5 + 3) = 16 cm.<\/p>\n<h3><span class=\"ez-toc-section\" id=\"42_Ung_dung_cua_tiep_tuyen_trong_kinh_te\"><\/span>4.2 \u1ee8ng d\u1ee5ng c\u1ee7a ti\u1ebfp tuy\u1ebfn trong kinh t\u1ebf<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p>Trong kinh t\u1ebf, ti\u1ebfp tuy\u1ebfn \u0111\u01b0\u1ee3c s\u1eed d\u1ee5ng \u0111\u1ec3 x\u00e1c \u0111\u1ecbnh c\u00e1c \u0111i\u1ec3m quan tr\u1ecdng tr\u00ean \u0111\u01b0\u1eddng cong ho\u1eb7c \u0111\u1ed3 th\u1ecb. Vi\u1ec7c x\u00e1c \u0111\u1ecbnh c\u00e1c \u0111i\u1ec3m n\u00e0y gi\u00fap ph\u00e2n t\u00edch v\u00e0 d\u1ef1 \u0111o\u00e1n xu h\u01b0\u1edbng ph\u00e1t tri\u1ec3n c\u1ee7a m\u1ed9t h\u1ec7 th\u1ed1ng kinh t\u1ebf.<\/p>\n<p>V\u00ed d\u1ee5, trong ph\u00e2n t\u00edch t\u00e0i ch\u00ednh, ti\u1ebfp tuy\u1ebfn c\u00f3 th\u1ec3 \u0111\u01b0\u1ee3c s\u1eed d\u1ee5ng \u0111\u1ec3 x\u00e1c \u0111\u1ecbnh \u0111i\u1ec3m c\u1ef1c tr\u1ecb c\u1ee7a m\u1ed9t bi\u1ec3u \u0111\u1ed3 ho\u1eb7c \u0111\u01b0\u1eddng cong. \u0110i\u1ec1u n\u00e0y gi\u00fap nh\u00e0 \u0111\u1ea7u t\u01b0 v\u00e0 c\u00e1c chuy\u00ean gia kinh t\u1ebf hi\u1ec3u r\u00f5 h\u01a1n v\u1ec1 xu h\u01b0\u1edbng v\u00e0 ti\u1ec1m n\u0103ng t\u0103ng tr\u01b0\u1edfng c\u1ee7a m\u1ed9t c\u00f4ng ty hay ng\u00e0nh c\u00f4ng nghi\u1ec7p.<\/p>\n<h2><span class=\"ez-toc-section\" id=\"5_Tinh_chat_tiep_tuyen_cua_duong_tron_va_cac_tinh_chat_lien_quan\"><\/span>5. T\u00ednh ch\u1ea5t ti\u1ebfp tuy\u1ebfn c\u1ee7a \u0111\u01b0\u1eddng tr\u00f2n v\u00e0 c\u00e1c t\u00ednh ch\u1ea5t li\u00ean quan.<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p><img decoding=\"async\" alt=\"5. T\u00ednh ch\u1ea5t ti\u1ebfp tuy\u1ebfn c\u1ee7a \u0111\u01b0\u1eddng tr\u00f2n v\u00e0 c\u00e1c t\u00ednh ch\u1ea5t li\u00ean quan.\" src=\"https:\/\/ungdung.hotronghiencuu.com\/open\/wp-content\/uploads\/2023\/09\/tiep_tuyen_dinh_nghia_tinh_chat_va_dau_hieu_nhan_biet_tiep_tuyen_duong_tron-1.jpg\" style=\"text-align: center; clear: both; display: block; margin: 0 auto;\" title=\"5. T\u00ednh ch\u1ea5t ti\u1ebfp tuy\u1ebfn c\u1ee7a \u0111\u01b0\u1eddng tr\u00f2n v\u00e0 c\u00e1c t\u00ednh ch\u1ea5t li\u00ean quan.\"\/><\/p>\n<h3><span class=\"ez-toc-section\" id=\"Tinh_chat_tiep_tuyen\"><\/span>T\u00ednh ch\u1ea5t ti\u1ebfp tuy\u1ebfn:<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p>\u0110\u01b0\u1eddng tr\u00f2n c\u00f3 m\u1ed9t \u0111\u01b0\u1eddng ti\u1ebfp tuy\u1ebfn duy nh\u1ea5t t\u1ea1i m\u1ed7i \u0111i\u1ec3m tr\u00ean \u0111\u01b0\u1eddng tr\u00f2n. \u0110i\u1ec1u n\u00e0y c\u00f3 ngh\u0129a l\u00e0 \u0111\u01b0\u1eddng ti\u1ebfp tuy\u1ebfn ch\u1ec9 c\u1eaft \u0111\u01b0\u1eddng tr\u00f2n \u1edf m\u1ed9t \u0111i\u1ec3m duy nh\u1ea5t v\u00e0 vu\u00f4ng g\u00f3c v\u1edbi b\u00e1n k\u00ednh \u0111i qua \u0111i\u1ec3m \u0111\u00f3.<\/p>\n<h3><span class=\"ez-toc-section\" id=\"Tinh_chat_lien_quan\"><\/span>T\u00ednh ch\u1ea5t li\u00ean quan:<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p>&#8211; G\u00f3c gi\u1eefa \u0111\u01b0\u1eddng ti\u1ebfp tuy\u1ebfn v\u00e0 b\u00e1n k\u00ednh \u0111i qua \u0111i\u1ec3m ti\u1ebfp x\u00fac l\u00e0 g\u00f3c vu\u00f4ng.<\/p>\n<p>&#8211; Hai \u0111\u01b0\u1eddng ti\u1ebfp tuy\u1ebfn c\u1ee7a hai \u0111\u01b0\u1eddng tr\u00f2n c\u1eaft nhau \u1edf m\u1ed9t \u0111i\u1ec3m duy nh\u1ea5t g\u1ecdi l\u00e0 \u0111i\u1ec3m c\u1eaft c\u1ee7a hai \u0111\u01b0\u1eddng tr\u00f2n.<\/p>\n<p>&#8211; \u0110\u1ed1i x\u1ee9ng qua m\u1ed9t \u0111\u01b0\u1eddng th\u1eb3ng ch\u1ee9a b\u00e1n k\u00ednh c\u1ee7a m\u1ed9t \u0111\u01b0\u1eddng tr\u00f2n s\u1ebd cho ta m\u1ed9t h\u00ecnh \u1ea3nh kh\u00e1c c\u1ee7a \u0111\u01b0\u1eddng tr\u00f2n ban \u0111\u1ea7u, trong \u0111\u00f3 c\u00e1c t\u00ednh ch\u1ea5t li\u00ean quan v\u1eabn \u0111\u01b0\u1ee3c gi\u1eef nguy\u00ean.<\/p>\n<h2><span class=\"ez-toc-section\" id=\"6_Cach_xac_dinh_goc_giua_hai_tiep_tuyen_va_cac_tinh_chat_lien_quan\"><\/span>6. C\u00e1ch x\u00e1c \u0111\u1ecbnh g\u00f3c gi\u1eefa hai ti\u1ebfp tuy\u1ebfn v\u00e0 c\u00e1c t\u00ednh ch\u1ea5t li\u00ean quan.<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<h3><span class=\"ez-toc-section\" id=\"Xac_dinh_goc_giua_hai_tiep_tuyen\"><\/span>X\u00e1c \u0111\u1ecbnh g\u00f3c gi\u1eefa hai ti\u1ebfp tuy\u1ebfn:<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p>\u0110\u1ec3 x\u00e1c \u0111\u1ecbnh g\u00f3c gi\u1eefa hai ti\u1ebfp tuy\u1ebfn c\u1ee7a \u0111\u01b0\u1eddng tr\u00f2n, ta s\u1eed d\u1ee5ng t\u00ednh ch\u1ea5t: &#8220;G\u00f3c n\u1ed9i ti\u1ebfp b\u1eb1ng m\u1ed9t n\u1eeda t\u1ed5ng c\u00e1c cung c\u00f3 chung \u0111\u1ec9nh v\u00e0 n\u1eb1m trong h\u00ecnh tr\u00f2n&#8221;.<\/p>\n<h3><span class=\"ez-toc-section\" id=\"Tinh_chat_lien_quan-2\"><\/span>T\u00ednh ch\u1ea5t li\u00ean quan:<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p>&#8211; G\u00f3c gi\u1eefa hai ti\u1ebfp tuy\u1ebfn c\u1ee7a \u0111\u01b0\u1eddng tr\u00f2n b\u1eb1ng m\u1ed9t n\u1eeda hi\u1ec7u c\u1ee7a hai cung c\u00f3 chung \u0111\u1ec9nh v\u00e0 n\u1eb1m trong h\u00ecnh tr\u00f2n.<\/p>\n<p>&#8211; Hai ti\u1ebfp tuy\u1ebfn c\u1ee7a c\u00f9ng m\u1ed9t \u0111\u01b0\u1eddng tr\u00f2n kh\u00f4ng th\u1ec3 song song v\u1edbi nhau.<\/p>\n<p>&#8211; G\u00f3c gi\u1eefa m\u1ed9t ti\u1ebfp tuy\u1ebfn v\u00e0 b\u00e1n k\u00ednh \u0111i qua \u0111i\u1ec3m ti\u1ebfp x\u00fac l\u00e0 g\u00f3c vu\u00f4ng.<\/p>\n<p>Ti\u1ebfp tuy\u1ebfn l\u00e0 m\u1ed9t kh\u00e1i ni\u1ec7m quan tr\u1ecdng trong to\u00e1n h\u1ecdc v\u00e0 v\u1eadt l\u00fd, \u0111\u1ec1 c\u1eadp \u0111\u1ebfn \u0111\u01b0\u1eddng th\u1eb3ng \u0111i qua hai \u0111i\u1ec3m tr\u00ean m\u1ed9t \u0111\u01b0\u1eddng cong. 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