{"id":567212,"date":"2026-07-21T09:21:25","date_gmt":"2026-07-21T02:21:25","guid":{"rendered":"https:\/\/hoanghamobile.com\/tin-tuc\/?p=567212"},"modified":"2026-07-21T09:21:25","modified_gmt":"2026-07-21T02:21:25","slug":"elip-la-gi","status":"publish","type":"post","link":"https:\/\/hoanghamobile.com\/tin-tuc\/elip-la-gi\/","title":{"rendered":"Elip l\u00e0 g\u00ec? Ph\u01b0\u01a1ng tr\u00ecnh ch\u00ednh t\u1eafc v\u00e0 c\u00e1c y\u1ebfu t\u1ed1"},"content":{"rendered":"<p><strong>Elip l\u00e0 t\u1eadp h\u1ee3p t\u1ea5t c\u1ea3 c\u00e1c \u0111i\u1ec3m trong m\u1eb7t ph\u1eb3ng c\u00f3 t\u1ed5ng kho\u1ea3ng c\u00e1ch \u0111\u1ebfn hai \u0111i\u1ec3m c\u1ed1 \u0111\u1ecbnh, g\u1ecdi l\u00e0 hai ti\u00eau \u0111i\u1ec3m, lu\u00f4n b\u1eb1ng m\u1ed9t h\u1eb1ng s\u1ed1 kh\u00f4ng \u0111\u1ed5i.<\/strong> Ph\u01b0\u01a1ng tr\u00ecnh ch\u00ednh t\u1eafc c\u1ee7a elip c\u00f3 d\u1ea1ng x\u00b2\/a\u00b2 + y\u00b2\/b\u00b2 = 1 (v\u1edbi a &gt; b &gt; 0). \u0110\u00e2y l\u00e0 ki\u1ebfn th\u1ee9c tr\u1ecdng t\u00e2m c\u1ee7a H\u00ecnh h\u1ecdc l\u1edbp 10, c\u0169ng l\u00e0 \u0111\u01b0\u1eddng cong m\u00f4 t\u1ea3 qu\u1ef9 \u0111\u1ea1o h\u00e0nh tinh trong V\u1eadt l\u00fd. N\u1ed9i dung d\u01b0\u1edbi \u0111\u00e2y tr\u00ecnh b\u00e0y elip l\u00e0 g\u00ec, ph\u01b0\u01a1ng tr\u00ecnh ch\u00ednh t\u1eafc, c\u00e1c y\u1ebfu t\u1ed1, t\u00e2m sai, di\u1ec7n t\u00edch &#8211; chu vi, c\u00e1ch vi\u1ebft ph\u01b0\u01a1ng tr\u00ecnh v\u00e0 b\u00e0i t\u1eadp v\u1eadn d\u1ee5ng c\u00f3 l\u1eddi gi\u1ea3i chi ti\u1ebft.<\/p>\n<h2>Elip l\u00e0 g\u00ec?<\/h2>\n<p>Cho hai \u0111i\u1ec3m c\u1ed1 \u0111\u1ecbnh F\u2081 v\u00e0 F\u2082 v\u1edbi kho\u1ea3ng c\u00e1ch F\u2081F\u2082 = 2c &gt; 0. Elip l\u00e0 t\u1eadp h\u1ee3p c\u00e1c \u0111i\u1ec3m M trong m\u1eb7t ph\u1eb3ng sao cho t\u1ed5ng kho\u1ea3ng c\u00e1ch MF\u2081 + MF\u2082 = 2a kh\u00f4ng \u0111\u1ed5i (v\u1edbi a &gt; c). Hai \u0111i\u1ec3m F\u2081 v\u00e0 F\u2082 \u0111\u01b0\u1ee3c g\u1ecdi l\u00e0 hai ti\u00eau \u0111i\u1ec3m c\u1ee7a elip, c\u00f2n \u0111o\u1ea1n F\u2081F\u2082 g\u1ecdi l\u00e0 ti\u00eau c\u1ef1. V\u1ec1 h\u00ecnh d\u1ea1ng, elip c\u00f3 th\u1ec3 \u0111\u01b0\u1ee3c h\u00ecnh dung nh\u01b0 m\u1ed9t \u0111\u01b0\u1eddng tr\u00f2n b\u1ecb k\u00e9o d\u00e0i ho\u1eb7c d\u1eb9t l\u1ea1i theo m\u1ed9t ph\u01b0\u01a1ng.<\/p>\n<p><img fetchpriority=\"high\" decoding=\"async\" class=\"size-full wp-image-568337 aligncenter\" src=\"https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2026\/07\/elip-la-gi-1.jpg\" alt=\"elip-la-gi-1\" width=\"800\" height=\"450\" srcset=\"https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2026\/07\/elip-la-gi-1.jpg 800w, https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2026\/07\/elip-la-gi-1-300x169.jpg 300w, https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2026\/07\/elip-la-gi-1-768x432.jpg 768w\" sizes=\"(max-width: 800px) 100vw, 800px\" \/><\/p>\n<h2>Ph\u01b0\u01a1ng tr\u00ecnh ch\u00ednh t\u1eafc c\u1ee7a elip<\/h2>\n<p>Khi ch\u1ecdn h\u1ec7 t\u1ecda \u0111\u1ed9 sao cho hai ti\u00eau \u0111i\u1ec3m n\u1eb1m tr\u00ean tr\u1ee5c ho\u00e0nh v\u00e0 \u0111\u1ed1i x\u1ee9ng qua g\u1ed1c t\u1ecda \u0111\u1ed9, elip c\u00f3 ph\u01b0\u01a1ng tr\u00ecnh ch\u00ednh t\u1eafc:<\/p>\n<p><strong>x\u00b2\/a\u00b2 + y\u00b2\/b\u00b2 = 1 (v\u1edbi a &gt; b &gt; 0)<\/strong><\/p>\n<p>Trong \u0111\u00f3 a l\u00e0 b\u00e1n tr\u1ee5c l\u1edbn, b l\u00e0 b\u00e1n tr\u1ee5c nh\u1ecf, c\u00f2n c l\u00e0 n\u1eeda ti\u00eau c\u1ef1. Ba \u0111\u1ea1i l\u01b0\u1ee3ng n\u00e0y li\u00ean h\u1ec7 v\u1edbi nhau qua h\u1ec7 th\u1ee9c <strong>b\u00b2 = a\u00b2 \u2212 c\u00b2<\/strong>, hay vi\u1ebft c\u00e1ch kh\u00e1c l\u00e0 a\u00b2 = b\u00b2 + c\u00b2. Ch\u1ec9 c\u1ea7n bi\u1ebft hai trong ba gi\u00e1 tr\u1ecb a, b, c l\u00e0 b\u1ea1n t\u00ednh \u0111\u01b0\u1ee3c gi\u00e1 tr\u1ecb c\u00f2n l\u1ea1i v\u00e0 vi\u1ebft ngay \u0111\u01b0\u1ee3c ph\u01b0\u01a1ng tr\u00ecnh.<\/p>\n<p>M\u1ed9t \u0111i\u1ec3m M(x\u2080; y\u2080) thu\u1ed9c elip khi v\u00e0 ch\u1ec9 khi t\u1ecda \u0111\u1ed9 c\u1ee7a n\u00f3 th\u1ecfa m\u00e3n ph\u01b0\u01a1ng tr\u00ecnh. V\u00ed d\u1ee5, x\u00e9t elip x\u00b2\/25 + y\u00b2\/9 = 1 v\u00e0 \u0111i\u1ec3m M(3; 2,4): thay v\u00e0o ta c\u00f3 9\/25 + 5,76\/9 = 0,36 + 0,64 = 1, v\u1eady M n\u1eb1m tr\u00ean elip.<\/p>\n<p><img decoding=\"async\" class=\"size-full wp-image-568338 aligncenter\" src=\"https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2026\/07\/elip-la-gi-2.jpg\" alt=\"elip-la-gi-2\" width=\"800\" height=\"450\" srcset=\"https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2026\/07\/elip-la-gi-2.jpg 800w, https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2026\/07\/elip-la-gi-2-300x169.jpg 300w, https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2026\/07\/elip-la-gi-2-768x432.jpg 768w\" sizes=\"(max-width: 800px) 100vw, 800px\" \/><\/p>\n<h2>C\u00e1c y\u1ebfu t\u1ed1 c\u1ee7a elip<\/h2>\n<p>T\u1eeb ph\u01b0\u01a1ng tr\u00ecnh ch\u00ednh t\u1eafc, b\u1ea1n x\u00e1c \u0111\u1ecbnh \u0111\u01b0\u1ee3c to\u00e0n b\u1ed9 c\u00e1c y\u1ebfu t\u1ed1 h\u00ecnh h\u1ecdc c\u1ee7a elip theo b\u1ea3ng sau.<\/p>\n<table>\n<thead>\n<tr>\n<th>Y\u1ebfu t\u1ed1<\/th>\n<th>Gi\u00e1 tr\u1ecb<\/th>\n<\/tr>\n<\/thead>\n<tbody>\n<tr>\n<td>Tr\u1ee5c l\u1edbn<\/td>\n<td>\u0110\u1ed9 d\u00e0i 2a (n\u1eb1m tr\u00ean tr\u1ee5c ho\u00e0nh)<\/td>\n<\/tr>\n<tr>\n<td>Tr\u1ee5c nh\u1ecf<\/td>\n<td>\u0110\u1ed9 d\u00e0i 2b (n\u1eb1m tr\u00ean tr\u1ee5c tung)<\/td>\n<\/tr>\n<tr>\n<td>Ti\u00eau c\u1ef1<\/td>\n<td>F\u2081F\u2082 = 2c, v\u1edbi c\u00b2 = a\u00b2 \u2212 b\u00b2<\/td>\n<\/tr>\n<tr>\n<td>Hai ti\u00eau \u0111i\u1ec3m<\/td>\n<td>F\u2081(\u2212c; 0) v\u00e0 F\u2082(c; 0)<\/td>\n<\/tr>\n<tr>\n<td>B\u1ed1n \u0111\u1ec9nh<\/td>\n<td>A\u2081(\u2212a; 0), A\u2082(a; 0), B\u2081(0; \u2212b), B\u2082(0; b)<\/td>\n<\/tr>\n<tr>\n<td>T\u00e2m \u0111\u1ed1i x\u1ee9ng<\/td>\n<td>G\u1ed1c t\u1ecda \u0111\u1ed9 O(0; 0)<\/td>\n<\/tr>\n<tr>\n<td>Tr\u1ee5c \u0111\u1ed1i x\u1ee9ng<\/td>\n<td>Tr\u1ee5c ho\u00e0nh v\u00e0 tr\u1ee5c tung<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<h2>T\u00e2m sai c\u1ee7a elip<\/h2>\n<p>T\u00e2m sai, k\u00fd hi\u1ec7u l\u00e0 e, l\u00e0 t\u1ec9 s\u1ed1 gi\u1eefa kho\u1ea3ng c\u00e1ch t\u1eeb t\u00e2m \u0111\u1ebfn m\u1ed9t ti\u00eau \u0111i\u1ec3m v\u00e0 b\u00e1n tr\u1ee5c l\u1edbn, \u0111\u01b0\u1ee3c t\u00ednh theo c\u00f4ng th\u1ee9c <strong>e = c\/a<\/strong>. V\u00ec 0 &lt; c &lt; a n\u00ean t\u00e2m sai c\u1ee7a elip lu\u00f4n th\u1ecfa m\u00e3n 0 &lt; e &lt; 1. T\u00e2m sai cho bi\u1ebft m\u1ee9c \u0111\u1ed9 d\u1eb9t c\u1ee7a elip: e c\u00e0ng g\u1ea7n 0 th\u00ec elip c\u00e0ng g\u1ea7n v\u1edbi \u0111\u01b0\u1eddng tr\u00f2n, c\u00f2n e c\u00e0ng g\u1ea7n 1 th\u00ec elip c\u00e0ng d\u1eb9t.<\/p>\n<p>T\u00e2m sai c\u00f2n gi\u00fap t\u00ednh nhanh b\u00e1n k\u00ednh qua ti\u00eau, t\u1ee9c kho\u1ea3ng c\u00e1ch t\u1eeb m\u1ed9t \u0111i\u1ec3m M(x\u2080; y\u2080) tr\u00ean elip \u0111\u1ebfn hai ti\u00eau \u0111i\u1ec3m: MF\u2081 = a + e\u00b7x\u2080 v\u00e0 MF\u2082 = a \u2212 e\u00b7x\u2080. C\u1ed9ng hai bi\u1ec3u th\u1ee9c l\u1ea1i lu\u00f4n \u0111\u01b0\u1ee3c 2a, \u0111\u00fang v\u1edbi \u0111\u1ecbnh ngh\u0129a ban \u0111\u1ea7u c\u1ee7a elip.<\/p>\n<p><img decoding=\"async\" class=\"size-full wp-image-568339 aligncenter\" src=\"https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2026\/07\/elip-la-gi-3.jpg\" alt=\"elip-la-gi-3\" width=\"800\" height=\"450\" srcset=\"https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2026\/07\/elip-la-gi-3.jpg 800w, https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2026\/07\/elip-la-gi-3-300x169.jpg 300w, https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2026\/07\/elip-la-gi-3-768x432.jpg 768w\" sizes=\"(max-width: 800px) 100vw, 800px\" \/><\/p>\n<h2>Di\u1ec7n t\u00edch v\u00e0 chu vi h\u00ecnh elip<\/h2>\n<p>Di\u1ec7n t\u00edch h\u00ecnh elip \u0111\u01b0\u1ee3c t\u00ednh r\u1ea5t g\u1ecdn b\u1eb1ng c\u00f4ng th\u1ee9c <strong>S = \u03c0 \u00d7 a \u00d7 b<\/strong>, trong \u0111\u00f3 a v\u00e0 b l\u00e0 hai b\u00e1n tr\u1ee5c. Khi a = b, c\u00f4ng th\u1ee9c tr\u1edf v\u1ec1 \u0111\u00fang S = \u03c0R\u00b2 c\u1ee7a h\u00ecnh tr\u00f2n.<\/p>\n<ul>\n<li><strong>V\u00ed d\u1ee5:<\/strong> elip x\u00b2\/25 + y\u00b2\/9 = 1 c\u00f3 a = 5, b = 3 n\u00ean S = \u03c0 \u00d7 5 \u00d7 3 = 15\u03c0 \u2248 47,12 \u0111\u01a1n v\u1ecb di\u1ec7n t\u00edch.<\/li>\n<li><strong>V\u00ed d\u1ee5:<\/strong> elip x\u00b2\/16 + y\u00b2\/9 = 1 c\u00f3 a = 4, b = 3 n\u00ean S = 12\u03c0 \u2248 37,70 \u0111\u01a1n v\u1ecb di\u1ec7n t\u00edch.<\/li>\n<\/ul>\n<p>Chu vi elip kh\u00f4ng c\u00f3 c\u00f4ng th\u1ee9c s\u01a1 c\u1ea5p g\u1ecdn nh\u01b0 di\u1ec7n t\u00edch, n\u00ean ng\u01b0\u1eddi ta th\u01b0\u1eddng d\u00f9ng c\u00f4ng th\u1ee9c g\u1ea7n \u0111\u00fang c\u1ee7a Ramanujan: C \u2248 \u03c0 \u00d7 [3(a + b) \u2212 \u221a((3a + b)(a + 3b))]. V\u1edbi a = 5 v\u00e0 b = 3, ta c\u00f3 3(a + b) = 24, (3a + b)(a + 3b) = 18 \u00d7 14 = 252, \u221a252 \u2248 15,87, n\u00ean C \u2248 \u03c0 \u00d7 8,13 \u2248 25,53 \u0111\u01a1n v\u1ecb \u0111\u1ed9 d\u00e0i.<\/p>\n<h2>V\u00ed d\u1ee5 v\u1ec1 elip<\/h2>\n<ul>\n<li><strong>V\u00ed d\u1ee5 1:<\/strong> Elip x\u00b2\/25 + y\u00b2\/9 = 1 c\u00f3 a\u00b2 = 25, b\u00b2 = 9 n\u00ean a = 5, b = 3; c\u00b2 = a\u00b2 \u2212 b\u00b2 = 16 n\u00ean c = 4. Tr\u1ee5c l\u1edbn 2a = 10, tr\u1ee5c nh\u1ecf 2b = 6, ti\u00eau c\u1ef1 2c = 8, hai ti\u00eau \u0111i\u1ec3m l\u00e0 F\u2081(\u22124; 0) v\u00e0 F\u2082(4; 0).<\/li>\n<li><strong>V\u00ed d\u1ee5 2:<\/strong> Elip tr\u00ean c\u00f3 t\u00e2m sai e = c\/a = 4\/5 = 0,8, t\u1ee9c l\u00e0 kh\u00e1 d\u1eb9t. V\u1edbi \u0111i\u1ec3m M(3; 2,4) n\u1eb1m tr\u00ean elip, b\u00e1n k\u00ednh qua ti\u00eau l\u00e0 MF\u2081 = 5 + 0,8 \u00d7 3 = 7,4 v\u00e0 MF\u2082 = 5 \u2212 0,8 \u00d7 3 = 2,6; t\u1ed5ng b\u1eb1ng 10 = 2a.<\/li>\n<\/ul>\n<h2>C\u00e1ch vi\u1ebft ph\u01b0\u01a1ng tr\u00ecnh ch\u00ednh t\u1eafc c\u1ee7a elip<\/h2>\n<p>D\u00f9 \u0111\u1ec1 b\u00e0i cho d\u1eef ki\u1ec7n n\u00e0o, b\u1ea1n c\u0169ng ch\u1ec9 c\u1ea7n quy v\u1ec1 vi\u1ec7c t\u00ecm a\u00b2 v\u00e0 b\u00b2, r\u1ed3i thay v\u00e0o d\u1ea1ng x\u00b2\/a\u00b2 + y\u00b2\/b\u00b2 = 1. Ba d\u1ea1ng th\u01b0\u1eddng g\u1eb7p:<\/p>\n<ul>\n<li><strong>D\u1ea1ng 1 &#8211; bi\u1ebft \u0111\u1ed9 d\u00e0i hai tr\u1ee5c:<\/strong> tr\u1ee5c l\u1edbn b\u1eb1ng 10, tr\u1ee5c nh\u1ecf b\u1eb1ng 6 th\u00ec a = 5, b = 3, ph\u01b0\u01a1ng tr\u00ecnh l\u00e0 x\u00b2\/25 + y\u00b2\/9 = 1.<\/li>\n<li><strong>D\u1ea1ng 2 &#8211; bi\u1ebft m\u1ed9t tr\u1ee5c v\u00e0 ti\u00eau \u0111i\u1ec3m:<\/strong> elip c\u00f3 ti\u00eau \u0111i\u1ec3m F(4; 0) v\u00e0 \u0111i qua \u0111i\u1ec3m B(0; 3). V\u00ec B n\u1eb1m tr\u00ean tr\u1ee5c tung n\u00ean b = 3, l\u1ea1i c\u00f3 c = 4 n\u00ean a\u00b2 = b\u00b2 + c\u00b2 = 9 + 16 = 25, ph\u01b0\u01a1ng tr\u00ecnh l\u00e0 x\u00b2\/25 + y\u00b2\/9 = 1.<\/li>\n<li><strong>D\u1ea1ng 3 &#8211; bi\u1ebft t\u00e2m sai v\u00e0 m\u1ed9t tr\u1ee5c:<\/strong> elip c\u00f3 t\u00e2m sai e = 0,6 v\u00e0 tr\u1ee5c l\u1edbn b\u1eb1ng 10. Khi \u0111\u00f3 a = 5, c = e \u00d7 a = 3, suy ra b\u00b2 = 25 \u2212 9 = 16, ph\u01b0\u01a1ng tr\u00ecnh l\u00e0 x\u00b2\/25 + y\u00b2\/16 = 1.<\/li>\n<\/ul>\n<p><strong>Xem th\u00eam: <a href=\"https:\/\/hoanghamobile.com\/tin-tuc\/dien-tich-hinh-tron\/\">C\u00f4ng Th\u1ee9c T\u00ednh Di\u1ec7n T\u00edch H\u00ecnh Tr\u00f2n: C\u00e1ch T\u00ednh, V\u00ed D\u1ee5 &amp; B\u00e0i T\u1eadp<\/a><\/strong><\/p>\n<h2>B\u00e0i t\u1eadp v\u1eadn d\u1ee5ng c\u00f3 l\u1eddi gi\u1ea3i<\/h2>\n<ul>\n<li><strong>B\u00e0i 1:<\/strong> Cho elip x\u00b2\/16 + y\u00b2\/4 = 1. T\u00ecm a, b, c. <em>L\u1eddi gi\u1ea3i:<\/em> a\u00b2 = 16 n\u00ean a = 4; b\u00b2 = 4 n\u00ean b = 2; c\u00b2 = a\u00b2 \u2212 b\u00b2 = 16 \u2212 4 = 12 n\u00ean c = 2\u221a3 \u2248 3,46.<\/li>\n<li><strong>B\u00e0i 2:<\/strong> T\u00ednh \u0111\u1ed9 d\u00e0i tr\u1ee5c l\u1edbn v\u00e0 tr\u1ee5c nh\u1ecf c\u1ee7a elip x\u00b2\/36 + y\u00b2\/25 = 1. <em>L\u1eddi gi\u1ea3i:<\/em> a\u00b2 = 36 n\u00ean a = 6; b\u00b2 = 25 n\u00ean b = 5. Tr\u1ee5c l\u1edbn 2a = 12, tr\u1ee5c nh\u1ecf 2b = 10.<\/li>\n<li><strong>B\u00e0i 3:<\/strong> Elip c\u00f3 a = 5, c = 3. Vi\u1ebft ph\u01b0\u01a1ng tr\u00ecnh ch\u00ednh t\u1eafc. <em>L\u1eddi gi\u1ea3i:<\/em> b\u00b2 = a\u00b2 \u2212 c\u00b2 = 25 \u2212 9 = 16, v\u1eady ph\u01b0\u01a1ng tr\u00ecnh l\u00e0 x\u00b2\/25 + y\u00b2\/16 = 1.<\/li>\n<li><strong>B\u00e0i 4:<\/strong> T\u00ecm t\u1ecda \u0111\u1ed9 hai ti\u00eau \u0111i\u1ec3m c\u1ee7a elip x\u00b2\/100 + y\u00b2\/64 = 1. <em>L\u1eddi gi\u1ea3i:<\/em> a = 10, b = 8, c\u00b2 = 100 \u2212 64 = 36 n\u00ean c = 6. Hai ti\u00eau \u0111i\u1ec3m l\u00e0 F\u2081(\u22126; 0) v\u00e0 F\u2082(6; 0).<\/li>\n<li><strong>B\u00e0i 5:<\/strong> T\u00ednh di\u1ec7n t\u00edch h\u00ecnh elip x\u00b2\/49 + y\u00b2\/25 = 1. <em>L\u1eddi gi\u1ea3i:<\/em> a = 7, b = 5 n\u00ean S = \u03c0 \u00d7 7 \u00d7 5 = 35\u03c0 \u2248 109,96 \u0111\u01a1n v\u1ecb di\u1ec7n t\u00edch.<\/li>\n<li><strong>B\u00e0i 6 (tr\u1eafc nghi\u1ec7m):<\/strong> T\u00e2m sai c\u1ee7a elip x\u00b2\/25 + y\u00b2\/16 = 1 b\u1eb1ng bao nhi\u00eau? A. 0,6 \u2014 B. 0,8 \u2014 C. 0,5 \u2014 D. 1. <em>\u0110\u00e1p \u00e1n:<\/em> A, v\u00ec c\u00b2 = 25 \u2212 16 = 9 n\u00ean c = 3, a = 5 v\u00e0 e = 3\/5 = 0,6.<\/li>\n<\/ul>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"size-full wp-image-568340 aligncenter\" src=\"https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2026\/07\/elip-la-gi-4.jpg\" alt=\"elip-la-gi-4\" width=\"800\" height=\"450\" srcset=\"https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2026\/07\/elip-la-gi-4.jpg 800w, https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2026\/07\/elip-la-gi-4-300x169.jpg 300w, https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2026\/07\/elip-la-gi-4-768x432.jpg 768w\" sizes=\"(max-width: 800px) 100vw, 800px\" \/><\/p>\n<h2>C\u00e1ch v\u1ebd elip v\u00e0 \u1ee9ng d\u1ee5ng<\/h2>\n<p>B\u1ea1n c\u00f3 th\u1ec3 v\u1ebd elip b\u1eb1ng c\u00e1ch c\u1ed1 \u0111\u1ecbnh hai chi\u1ebfc \u0111inh t\u1ea1i hai ti\u00eau \u0111i\u1ec3m, sau \u0111\u00f3 bu\u1ed9c m\u1ed9t s\u1ee3i d\u00e2y c\u00f3 \u0111\u1ed9 d\u00e0i c\u1ed1 \u0111\u1ecbnh v\u00e0o hai chi\u1ebfc \u0111inh. Khi d\u00f9ng b\u00fat gi\u1eef c\u0103ng s\u1ee3i d\u00e2y v\u00e0 di chuy\u1ec3n xung quanh, \u0111\u1ea7u b\u00fat s\u1ebd v\u1ea1ch n\u00ean m\u1ed9t \u0111\u01b0\u1eddng elip, v\u00ec t\u1ed5ng kho\u1ea3ng c\u00e1ch t\u1eeb m\u1ecdi \u0111i\u1ec3m tr\u00ean \u0111\u01b0\u1eddng v\u1ebd \u0111\u1ebfn hai ti\u00eau \u0111i\u1ec3m lu\u00f4n b\u1eb1ng \u0111\u1ed9 d\u00e0i s\u1ee3i d\u00e2y. \u0110\u1ed9 d\u00e0i d\u00e2y ch\u00ednh l\u00e0 2a, c\u00f2n kho\u1ea3ng c\u00e1ch gi\u1eefa hai \u0111inh ch\u00ednh l\u00e0 2c.<\/p>\n<p>Trong th\u1ef1c t\u1ebf, elip xu\u1ea5t hi\u1ec7n \u1edf nhi\u1ec1u n\u01a1i: qu\u1ef9 \u0111\u1ea1o chuy\u1ec3n \u0111\u1ed9ng c\u1ee7a c\u00e1c h\u00e0nh tinh quanh M\u1eb7t Tr\u1eddi theo \u0111\u1ecbnh lu\u1eadt Kepler, thi\u1ebft k\u1ebf th\u1ea5u k\u00ednh v\u00e0 g\u01b0\u01a1ng ph\u1ea3n x\u1ea1, m\u1eb7t c\u1eaft c\u1ee7a \u1ed1ng nghi\u00eang, v\u00f2m tr\u1ea7n ki\u1ec3u &#8220;ph\u00f2ng th\u00ec th\u1ea7m&#8221; hay \u0111\u01b0\u1eddng bi\u00ean c\u1ee7a nhi\u1ec1u s\u00e2n v\u1eadn \u0111\u1ed9ng.<\/p>\n<h2>Ph\u00e2n bi\u1ec7t elip v\u00e0 \u0111\u01b0\u1eddng tr\u00f2n<\/h2>\n<p>\u0110\u01b0\u1eddng tr\u00f2n l\u00e0 m\u1ed9t tr\u01b0\u1eddng h\u1ee3p \u0111\u1eb7c bi\u1ec7t c\u1ee7a elip khi hai ti\u00eau \u0111i\u1ec3m tr\u00f9ng nhau, t\u1ee9c c = 0. B\u1ea3ng d\u01b0\u1edbi \u0111\u00e2y t\u00f3m t\u1eaft kh\u00e1c bi\u1ec7t gi\u1eefa hai \u0111\u01b0\u1eddng cong n\u00e0y.<\/p>\n<table>\n<thead>\n<tr>\n<th>Ti\u00eau ch\u00ed<\/th>\n<th>Elip<\/th>\n<th>\u0110\u01b0\u1eddng tr\u00f2n<\/th>\n<\/tr>\n<\/thead>\n<tbody>\n<tr>\n<td>Ti\u00eau \u0111i\u1ec3m<\/td>\n<td>Hai ti\u00eau \u0111i\u1ec3m ph\u00e2n bi\u1ec7t<\/td>\n<td>Hai ti\u00eau \u0111i\u1ec3m tr\u00f9ng nhau t\u1ea1i t\u00e2m<\/td>\n<\/tr>\n<tr>\n<td>Quan h\u1ec7 a, b<\/td>\n<td>a &gt; b<\/td>\n<td>a = b = R<\/td>\n<\/tr>\n<tr>\n<td>T\u00e2m sai<\/td>\n<td>0 &lt; e &lt; 1<\/td>\n<td>e = 0<\/td>\n<\/tr>\n<tr>\n<td>Ph\u01b0\u01a1ng tr\u00ecnh<\/td>\n<td>x\u00b2\/a\u00b2 + y\u00b2\/b\u00b2 = 1<\/td>\n<td>x\u00b2 + y\u00b2 = R\u00b2<\/td>\n<\/tr>\n<tr>\n<td>Di\u1ec7n t\u00edch<\/td>\n<td>S = \u03c0ab<\/td>\n<td>S = \u03c0R\u00b2<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p><strong>Xem th\u00eam: <a href=\"https:\/\/hoanghamobile.com\/tin-tuc\/dien-tich-xung-quanh-hinh-tru\/\">Di\u1ec7n t\u00edch xung quanh h\u00ecnh tr\u1ee5 v\u00e0 \u1ee9ng d\u1ee5ng<\/a><\/strong><\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"size-full wp-image-568341 aligncenter\" src=\"https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2026\/07\/elip-la-gi-5.jpg\" alt=\"elip-la-gi-5\" width=\"800\" height=\"450\" srcset=\"https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2026\/07\/elip-la-gi-5.jpg 800w, https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2026\/07\/elip-la-gi-5-300x169.jpg 300w, https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2026\/07\/elip-la-gi-5-768x432.jpg 768w\" sizes=\"(max-width: 800px) 100vw, 800px\" \/><\/p>\n<h2>C\u00e2u h\u1ecfi th\u01b0\u1eddng g\u1eb7p v\u1ec1 elip<\/h2>\n<h3>Elip l\u00e0 g\u00ec?<\/h3>\n<p>L\u00e0 t\u1eadp h\u1ee3p c\u00e1c \u0111i\u1ec3m trong m\u1eb7t ph\u1eb3ng c\u00f3 t\u1ed5ng kho\u1ea3ng c\u00e1ch \u0111\u1ebfn hai ti\u00eau \u0111i\u1ec3m lu\u00f4n b\u1eb1ng m\u1ed9t h\u1eb1ng s\u1ed1 2a.<\/p>\n<h3>Ph\u01b0\u01a1ng tr\u00ecnh ch\u00ednh t\u1eafc c\u1ee7a elip l\u00e0 g\u00ec?<\/h3>\n<p>Ph\u01b0\u01a1ng tr\u00ecnh ch\u00ednh t\u1eafc c\u1ee7a elip l\u00e0 x\u00b2\/a\u00b2 + y\u00b2\/b\u00b2 = 1 v\u1edbi a &gt; b &gt; 0.<\/p>\n<h3>H\u1ec7 th\u1ee9c gi\u1eefa a, b, c c\u1ee7a elip l\u00e0 g\u00ec?<\/h3>\n<p>H\u1ec7 th\u1ee9c l\u00e0 b\u00b2 = a\u00b2 \u2212 c\u00b2, trong \u0111\u00f3 2c l\u00e0 ti\u00eau c\u1ef1 v\u00e0 2a l\u00e0 \u0111\u1ed9 d\u00e0i tr\u1ee5c l\u1edbn.<\/p>\n<h3>T\u00e2m sai c\u1ee7a elip l\u00e0 g\u00ec?<\/h3>\n<p>T\u00e2m sai l\u00e0 e = c\/a, lu\u00f4n th\u1ecfa m\u00e3n 0 &lt; e &lt; 1; e c\u00e0ng l\u1edbn th\u00ec elip c\u00e0ng d\u1eb9t.<\/p>\n<h3>\u0110\u01b0\u1eddng tr\u00f2n c\u00f3 ph\u1ea3i elip kh\u00f4ng?<\/h3>\n<p>C\u00f3, \u0111\u01b0\u1eddng tr\u00f2n l\u00e0 elip \u0111\u1eb7c bi\u1ec7t khi hai ti\u00eau \u0111i\u1ec3m tr\u00f9ng nhau, khi \u0111\u00f3 c = 0, a = b v\u00e0 e = 0.<\/p>\n<h3>C\u00f4ng th\u1ee9c t\u00ednh di\u1ec7n t\u00edch h\u00ecnh elip l\u00e0 g\u00ec?<\/h3>\n<p>Di\u1ec7n t\u00edch h\u00ecnh elip b\u1eb1ng S = \u03c0ab, v\u1edbi a v\u00e0 b l\u1ea7n l\u01b0\u1ee3t l\u00e0 b\u00e1n tr\u1ee5c l\u1edbn v\u00e0 b\u00e1n tr\u1ee5c nh\u1ecf.<\/p>\n<h3>L\u00e0m sao bi\u1ebft m\u1ed9t \u0111i\u1ec3m c\u00f3 thu\u1ed9c elip hay kh\u00f4ng?<\/h3>\n<p>Thay t\u1ecda \u0111\u1ed9 \u0111i\u1ec3m \u0111\u00f3 v\u00e0o ph\u01b0\u01a1ng tr\u00ecnh ch\u00ednh t\u1eafc, n\u1ebfu v\u1ebf tr\u00e1i b\u1eb1ng 1 th\u00ec \u0111i\u1ec3m thu\u1ed9c elip.<\/p>\n<p><script type=\"application\/ld+json\">\n{\n  \"@context\": \"https:\/\/schema.org\",\n  \"@type\": \"FAQPage\",\n  \"mainEntity\": [\n    {\n      \"@type\": \"Question\",\n      \"name\": \"Elip l\u00e0 g\u00ec?\",\n      \"acceptedAnswer\": {\n        \"@type\": \"Answer\",\n        \"text\": \"L\u00e0 t\u1eadp h\u1ee3p c\u00e1c \u0111i\u1ec3m trong m\u1eb7t ph\u1eb3ng c\u00f3 t\u1ed5ng kho\u1ea3ng c\u00e1ch \u0111\u1ebfn hai ti\u00eau \u0111i\u1ec3m lu\u00f4n b\u1eb1ng m\u1ed9t h\u1eb1ng s\u1ed1 2a.\"\n      }\n    },\n    {\n      \"@type\": \"Question\",\n      \"name\": \"Ph\u01b0\u01a1ng tr\u00ecnh ch\u00ednh t\u1eafc c\u1ee7a elip l\u00e0 g\u00ec?\",\n      \"acceptedAnswer\": {\n        \"@type\": \"Answer\",\n        \"text\": \"Ph\u01b0\u01a1ng tr\u00ecnh ch\u00ednh t\u1eafc c\u1ee7a elip l\u00e0 x\u00b2\/a\u00b2 + y\u00b2\/b\u00b2 = 1 v\u1edbi a > b > 0.\"\n      }\n    },\n    {\n      \"@type\": \"Question\",\n      \"name\": \"H\u1ec7 th\u1ee9c gi\u1eefa a, b, c c\u1ee7a elip l\u00e0 g\u00ec?\",\n      \"acceptedAnswer\": {\n        \"@type\": \"Answer\",\n        \"text\": \"H\u1ec7 th\u1ee9c l\u00e0 b\u00b2 = a\u00b2 \u2212 c\u00b2, trong \u0111\u00f3 2c l\u00e0 ti\u00eau c\u1ef1 v\u00e0 2a l\u00e0 \u0111\u1ed9 d\u00e0i tr\u1ee5c l\u1edbn.\"\n      }\n    },\n    {\n      \"@type\": \"Question\",\n      \"name\": \"T\u00e2m sai c\u1ee7a elip l\u00e0 g\u00ec?\",\n      \"acceptedAnswer\": {\n        \"@type\": \"Answer\",\n        \"text\": \"T\u00e2m sai l\u00e0 e = c\/a, lu\u00f4n th\u1ecfa m\u00e3n 0 < e < 1; e c\u00e0ng l\u1edbn th\u00ec elip c\u00e0ng d\u1eb9t.\"\n      }\n    },\n    {\n      \"@type\": \"Question\",\n      \"name\": \"\u0110\u01b0\u1eddng tr\u00f2n c\u00f3 ph\u1ea3i elip kh\u00f4ng?\",\n      \"acceptedAnswer\": {\n        \"@type\": \"Answer\",\n        \"text\": \"C\u00f3, \u0111\u01b0\u1eddng tr\u00f2n l\u00e0 elip \u0111\u1eb7c bi\u1ec7t khi hai ti\u00eau \u0111i\u1ec3m tr\u00f9ng nhau, khi \u0111\u00f3 c = 0, a = b v\u00e0 e = 0.\"\n      }\n    },\n    {\n      \"@type\": \"Question\",\n      \"name\": \"C\u00f4ng th\u1ee9c t\u00ednh di\u1ec7n t\u00edch h\u00ecnh elip l\u00e0 g\u00ec?\",\n      \"acceptedAnswer\": {\n        \"@type\": \"Answer\",\n        \"text\": \"Di\u1ec7n t\u00edch h\u00ecnh elip b\u1eb1ng S = \u03c0ab, v\u1edbi a v\u00e0 b l\u1ea7n l\u01b0\u1ee3t l\u00e0 b\u00e1n tr\u1ee5c l\u1edbn v\u00e0 b\u00e1n tr\u1ee5c nh\u1ecf.\"\n      }\n    },\n    {\n      \"@type\": \"Question\",\n      \"name\": \"L\u00e0m sao bi\u1ebft m\u1ed9t \u0111i\u1ec3m c\u00f3 thu\u1ed9c elip hay kh\u00f4ng?\",\n      \"acceptedAnswer\": {\n        \"@type\": \"Answer\",\n        \"text\": \"Thay t\u1ecda \u0111\u1ed9 \u0111i\u1ec3m \u0111\u00f3 v\u00e0o ph\u01b0\u01a1ng tr\u00ecnh ch\u00ednh t\u1eafc, n\u1ebfu v\u1ebf tr\u00e1i b\u1eb1ng 1 th\u00ec \u0111i\u1ec3m thu\u1ed9c elip.\"\n      }\n    }\n  ]\n}\n<\/script><\/p>\n<h2>K\u1ebft lu\u1eadn<\/h2>\n<p>T\u00f3m l\u1ea1i, elip l\u00e0 t\u1eadp h\u1ee3p \u0111i\u1ec3m c\u00f3 t\u1ed5ng kho\u1ea3ng c\u00e1ch \u0111\u1ebfn hai ti\u00eau \u0111i\u1ec3m b\u1eb1ng 2a, v\u1edbi ph\u01b0\u01a1ng tr\u00ecnh ch\u00ednh t\u1eafc x\u00b2\/a\u00b2 + y\u00b2\/b\u00b2 = 1 v\u00e0 h\u1ec7 th\u1ee9c b\u00b2 = a\u00b2 \u2212 c\u00b2. Ch\u1ec9 c\u1ea7n nh\u1edb ba \u0111\u1ea1i l\u01b0\u1ee3ng a, b, c c\u00f9ng c\u00f4ng th\u1ee9c t\u00e2m sai e = c\/a v\u00e0 di\u1ec7n t\u00edch S = \u03c0ab, b\u1ea1n s\u1ebd x\u1eed l\u00fd g\u1ecdn h\u1ea7u h\u1ebft d\u1ea1ng b\u00e0i v\u1ec1 elip trong ch\u01b0\u01a1ng tr\u00ecnh l\u1edbp 10. \u0110\u1ec3 h\u1ecdc th\u00eam, m\u1eddi b\u1ea1n tham kh\u1ea3o c\u00e1c b\u00e0i <a href=\"https:\/\/hoanghamobile.com\/tin-tuc\/dien-tich-hinh-tron\/\">c\u00f4ng th\u1ee9c t\u00ednh di\u1ec7n t\u00edch h\u00ecnh tr\u00f2n<\/a>, <a href=\"https:\/\/hoanghamobile.com\/tin-tuc\/dien-tich-tam-giac\/\">c\u00f4ng th\u1ee9c t\u00ednh di\u1ec7n t\u00edch tam gi\u00e1c<\/a> v\u00e0 <a href=\"https:\/\/hoanghamobile.com\/tin-tuc\/1-nam-anh-sang-bang-bao-nhieu-km\/\">m\u1ed9t n\u0103m \u00e1nh s\u00e1ng b\u1eb1ng bao nhi\u00eau km<\/a> tr\u00ean chuy\u00ean m\u1ee5c tin t\u1ee9c c\u1ee7a Ho\u00e0ng H\u00e0 Mobile.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Elip l\u00e0 t\u1eadp h\u1ee3p t\u1ea5t c\u1ea3 c\u00e1c \u0111i\u1ec3m trong m\u1eb7t ph\u1eb3ng c\u00f3 t\u1ed5ng kho\u1ea3ng c\u00e1ch \u0111\u1ebfn hai \u0111i\u1ec3m c\u1ed1 \u0111\u1ecbnh, g\u1ecdi l\u00e0 hai ti\u00eau \u0111i\u1ec3m, lu\u00f4n b\u1eb1ng m\u1ed9t h\u1eb1ng s\u1ed1 kh\u00f4ng \u0111\u1ed5i. Ph\u01b0\u01a1ng tr\u00ecnh ch\u00ednh t\u1eafc c\u1ee7a elip c\u00f3 d\u1ea1ng x\u00b2\/a\u00b2 + y\u00b2\/b\u00b2 = 1 (v\u1edbi a &gt; b &gt; 0). \u0110\u00e2y l\u00e0 ki\u1ebfn th\u1ee9c [&hellip;]<\/p>\n","protected":false},"author":65,"featured_media":568336,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"_yoast_wpseo_focuskw":"elip l\u00e0 g\u00ec","_yoast_wpseo_title":"Elip l\u00e0 g\u00ec? Ph\u01b0\u01a1ng tr\u00ecnh v\u00e0 c\u00e1c y\u1ebfu t\u1ed1","_yoast_wpseo_metadesc":"Elip l\u00e0 g\u00ec? Ph\u01b0\u01a1ng tr\u00ecnh ch\u00ednh t\u1eafc x\u00b2\/a\u00b2 + y\u00b2\/b\u00b2 = 1, c\u00e1c y\u1ebfu t\u1ed1, t\u00e2m sai, di\u1ec7n t\u00edch elip v\u00e0 b\u00e0i t\u1eadp v\u1eadn d\u1ee5ng c\u00f3 l\u1eddi gi\u1ea3i chi ti\u1ebft cho h\u1ecdc sinh l\u1edbp 10.","footnotes":""},"categories":[16],"tags":[],"class_list":["post-567212","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-thu-thuat"],"yoast_head":"<!-- This site is optimized with the Yoast SEO Premium plugin v27.3 (Yoast SEO v27.4) - https:\/\/yoast.com\/product\/yoast-seo-premium-wordpress\/ -->\n<title>Elip l\u00e0 g\u00ec? Ph\u01b0\u01a1ng tr\u00ecnh v\u00e0 c\u00e1c y\u1ebfu t\u1ed1<\/title>\n<meta name=\"description\" content=\"Elip l\u00e0 g\u00ec? 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