{"article_info":{"article_id":122461,"cat_id":1161,"cat_title":"Chuyên đề học tập Toán 10 - Kết nối tri thức","publish_time":1667219580,"cat_id2":1161,"is_link":0,"thumbnail":"","title":"Giải bài 3.9 trang 52 Chuyên đề học tập Toán 10 - Kết nối tri thức với cuộc sống","label":"Bài 3.9 trang 52 Chuyên đề học tập Toán 10 - Kết nối tri thức với cuộc sống","alias":"giai-bai-39-trang-52-chuyen-de-hoc-tap-toan-10-ket-noi-tri-thuc-voi-cuoc-song","introtext":"Trong mặt phẳng tọa độ Oxy, cho hypebol (H) có phương trình chính tắc. Lập phương trình chính tắc của (H) trong mỗi trường hợp sau: ","content":"<style>\r\n.method-close-icon{position: relative;float: right;top: 6px;transform: rotate(270deg);-ms-transform:rotate(270deg);-moz-transform:rotate(270deg);-webkit-transform:rotate(270deg);-o-transform:rotate(270deg);}\r\n.method-open-icon{position: relative;float: right;top: 6px;}\r\n</style>\r\n<p><strong style=\"font-size: 16px;\">Đề bài</strong></p><p><font style=\"vertical-align: inherit;\"><font style=\"vertical-align: inherit;\">Trong mặt phẳng tọa độ Oxy, cho hypebol (H) có phương trình chính tắc. </font><font style=\"vertical-align: inherit;\">Lập phương trình chính tắc của (H) trong mỗi trường hợp sau:</font></font></p>\r\n<p><font style=\"vertical-align: inherit;\"><font style=\"vertical-align: inherit;\">a) (H) có nửa khung thực tế bằng 4, tiêu cự bằng 10.</font></font></p>\r\n<p><font style=\"vertical-align: inherit;\"><font style=\"vertical-align: inherit;\">b) (H) có tiêu cự bằng \\(2\\sqrt {13} \\), một đường tiệm cận là \\(y = \\frac{2}{3}x\\).</font></font></p>\r\n<p><font style=\"vertical-align: inherit;\"><font style=\"vertical-align: inherit;\">c) (H) có tâm sai bằng \\(e = \\sqrt 5 \\), và đi qua điểm \\((\\sqrt {10} ;6)\\).</font></font></p><div id=\"pos_end_question\"></div><div style=\"padding-top: 10px;padding-bottom: 2px;margin-bottom: 10px;\"><p class=\"show-detail-method\" style=\"background: #654bc2;text-align: center;border-radius:5px;padding: 10px;margin-bottom: 0px;\" onclick=\"showDetailMethod();\"><strong style=\"font-size: 16px;\">Phương pháp giải - Xem chi tiết</strong><img class=\"method-open-icon\" id=\"method_colapse_icon\" src=\"data:image/png;base64,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\"></p>  <div class=\"content_method_content\" style=\"padding: 10px 10px 5px 10px;border: dashed 1px #654bc2;border-top:none;\"><p>PTCT của hypebol \\(\\frac{{{x^2}}}{{{a^2}}} - \\frac{{{y^2}}}{{{b^2}}} = 1\\).</p>\r\n<p>+ Độ dài nửa trục bằng a.</p>\r\n<p>+ Tiêu cự bằng \\(2c = 2\\sqrt {{a^2} + {b^2}} \\).</p>\r\n<p>+ Hai đường tiệm cận \\(y =  \\pm \\frac{b}{a}x\\).</p>\r\n<p>+ Tâm sai của hypebol: \\(e = \\frac{c}{a}\\).</p>  </div>\r\n<script type=\"text/javascript\">\r\n    var is_open =true;\r\n    function showDetailMethod(){\r\n        if(is_open){\r\n            document.querySelector(\".content_method_content\").style.display='none';\r\n            document.getElementById(\"method_colapse_icon\").classList.remove(\"method-open-icon\");\r\n            document.getElementById(\"method_colapse_icon\").classList.add(\"method-close-icon\");\r\n        }else{\r\n            document.querySelector(\".content_method_content\").style.display='block';\r\n            document.getElementById(\"method_colapse_icon\").classList.remove(\"method-close-icon\");\r\n            document.getElementById(\"method_colapse_icon\").classList.add(\"method-open-icon\");\r\n        }\r\n        is_open = !is_open;\r\n    }\r\n</script>\r\n</div><p><strong style=\"font-size: 16px;\">Lời giải chi tiết</strong></p><p><span style=\"font-size: 14pt;\">a) </span></p>\r\n<p><span style=\"font-size: 14pt;\">+ Độ dài nửa trục bằng 4 </span><span class=\"MTConvertedEquation\">\\( \\Rightarrow a = 4\\)</span><span style=\"font-size: 14.0pt;\">.</span></p>\r\n<p><span style=\"font-size: 14pt;\">+ Tiêu cự bằng<span id=\"MathJax-Element-1011-Frame\" style=\"display: inline-block; overflow-wrap: normal; max-width: none; max-height: none; min-width: 0px; min-height: 0px; float: none; word-spacing: normal;\" data-mathml=\"&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mn&gt;10&lt;/mn&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;mi&gt;c&lt;/mi&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;msqrt&gt;&lt;mrow class=&quot;MJX-TeXAtom-ORD&quot;&gt;&lt;msup&gt;&lt;mn&gt;4&lt;/mn&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;/msup&gt;&lt;/mrow&gt;&lt;mo&gt;+&lt;/mo&gt;&lt;mrow class=&quot;MJX-TeXAtom-ORD&quot;&gt;&lt;msup&gt;&lt;mi&gt;b&lt;/mi&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;/msup&gt;&lt;/mrow&gt;&lt;/msqrt&gt;&lt;mo stretchy=&quot;false&quot;&gt;&amp;#x21D2;&lt;/mo&gt;&lt;mi&gt;b&lt;/mi&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mn&gt;3&lt;/mn&gt;&lt;/math&gt;\"><span id=\"MJXc-Node-10338\" style=\"display: inline-block; border-spacing: 0px;\"><span id=\"MJXc-Node-10339\" style=\"display: inline-block; box-sizing: content-box !important;\"><span id=\"MJXc-Node-10340\" style=\"display: inline-block; box-sizing: content-box !important;\"><span class=\"MTConvertedEquation\">\\(10 = 2c = 2\\sqrt {{a^2} + {b^2}} \\)</span></span></span></span></span></span></p>\r\n<p><span class=\"MTConvertedEquation\">\\(\\begin{array}{l} \\Leftrightarrow 10 = 2\\sqrt {{4^2} + {b^2}} \\\\ \\Leftrightarrow \\sqrt {{4^2} + {b^2}}  = 5\\\\ \\Leftrightarrow {4^2} + {b^2} = 25\\\\ \\Leftrightarrow {b^2} = 9\\\\ \\Rightarrow b = 3.\\end{array}\\)</span></p>\r\n<p><span class=\"mjxassistivemathml\"><span id=\"MJXc-Node-10363\" style=\"display: inline-block; border-spacing: 0px;\"><span style=\"font-size: 14pt; font-family: 'Cambria Math', 'serif'; border: 1pt none windowtext; padding: 0cm;\"><span id=\"MJXc-Node-10364\" style=\"display: inline-block; box-sizing: content-box !important;\"><span id=\"MathJax-Element-1012-Frame\" style=\"display: inline-block; overflow-wrap: normal; max-width: none; max-height: none; min-width: 0px; min-height: 0px; float: none; word-spacing: normal;\" data-mathml=\"&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mo stretchy=&quot;false&quot;&gt;&amp;#x21D2;&lt;/mo&gt;&lt;/math&gt;\"><span id=\"MJXc-Node-10365\" style=\"display: inline-block; box-sizing: content-box !important;\"><span style=\"box-sizing: content-box !important;\">⇒</span></span></span></span><span style=\"font-size: 14pt;\">PTCT của hypebol<span class=\"mjx-char\"><span id=\"MJXc-Node-10366\" style=\"display: inline-block; border-spacing: 0px;\"><span style=\"border: none windowtext 1.0pt; mso-border-alt: none windowtext 0cm; padding: 0cm;\"><span id=\"MJXc-Node-10367\" style=\"display: inline-block; box-sizing: content-box !important;\"><span id=\"MathJax-Element-1013-Frame\" style=\"display: inline-block; overflow-wrap: normal; max-width: none; max-height: none; min-width: 0px; min-height: 0px; float: none; word-spacing: normal;\" data-mathml=\"&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mfrac&gt;&lt;mrow class=&quot;MJX-TeXAtom-ORD&quot;&gt;&lt;mrow class=&quot;MJX-TeXAtom-ORD&quot;&gt;&lt;msup&gt;&lt;mi&gt;x&lt;/mi&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;/msup&gt;&lt;/mrow&gt;&lt;/mrow&gt;&lt;mrow class=&quot;MJX-TeXAtom-ORD&quot;&gt;&lt;mn&gt;16&lt;/mn&gt;&lt;/mrow&gt;&lt;/mfrac&gt;&lt;mo&gt;&amp;#x2212;&lt;/mo&gt;&lt;mfrac&gt;&lt;mrow class=&quot;MJX-TeXAtom-ORD&quot;&gt;&lt;mrow class=&quot;MJX-TeXAtom-ORD&quot;&gt;&lt;msup&gt;&lt;mi&gt;y&lt;/mi&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;/msup&gt;&lt;/mrow&gt;&lt;/mrow&gt;&lt;mn&gt;9&lt;/mn&gt;&lt;/mfrac&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;/math&gt;\"><span id=\"MJXc-Node-10368\" style=\"display: inline-block; box-sizing: content-box !important;\"><span style=\"display: inline-block; box-sizing: content-box !important;\"><span style=\"box-sizing: content-box !important;\"><span id=\"MJXc-Node-10369\" style=\"display: inline-block; box-sizing: content-box !important;\"><span id=\"MJXc-Node-10370\" style=\"display: inline-block; box-sizing: content-box !important;\"><span id=\"MJXc-Node-10371\" style=\"display: inline-block; box-sizing: content-box !important;\"><span id=\"MJXc-Node-10372\" style=\"display: inline-block; box-sizing: content-box !important;\"><span id=\"MJXc-Node-10373\" style=\"display: inline-block; box-sizing: content-box !important;\"><span style=\"display: inline-block; box-sizing: content-box !important;\"><span id=\"MJXc-Node-10374\" style=\"display: inline-block; box-sizing: content-box !important;\"><span style=\"box-sizing: content-box !important;\">  </span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></p>\r\n<p><span class=\"MTConvertedEquation\">\\(\\frac{{{x^2}}}{{{4^2}}} - \\frac{{{y^2}}}{{{3^2}}} = 1 \\Leftrightarrow \\frac{{{x^2}}}{{16}} - \\frac{{{y^2}}}{9} = 1.\\)</span></p>\r\n<p><span style=\"font-size: 14pt;\">b)</span></p>\r\n<p><span style=\"font-size: 14pt;\">+ Tiêu cự bằng <span id=\"MathJax-Element-1014-Frame\" style=\"display: inline-block; overflow-wrap: normal; max-width: none; max-height: none; min-width: 0px; min-height: 0px; float: none; word-spacing: normal;\" data-mathml=\"&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;msqrt&gt;&lt;mn&gt;13&lt;/mn&gt;&lt;/msqrt&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;mi&gt;c&lt;/mi&gt;&lt;mo stretchy=&quot;false&quot;&gt;&amp;#x21D2;&lt;/mo&gt;&lt;mi&gt;c&lt;/mi&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;msqrt&gt;&lt;mn&gt;13&lt;/mn&gt;&lt;/msqrt&gt;&lt;/math&gt;\"><span id=\"MJXc-Node-10391\" style=\"display: inline-block; border-spacing: 0px;\"><span id=\"MJXc-Node-10392\" style=\"display: inline-block; box-sizing: content-box !important;\"><span id=\"MJXc-Node-10393\" style=\"display: inline-block; box-sizing: content-box !important;\"><span class=\"MTConvertedEquation\">\\(2\\sqrt {13}  = 2c \\Rightarrow c = \\sqrt {13} .\\)</span></span></span></span></span></span></p>\r\n<p><span style=\"font-size: 14pt;\">+ Ta có: </span><span class=\"MTConvertedEquation\">\\(2\\sqrt {13}  = 2c = 2\\sqrt {{a^2} + {b^2}} \\)</span></p>\r\n<p><span class=\"MTConvertedEquation\">\\(\\begin{array}{l} \\Leftrightarrow \\sqrt {13}  = \\sqrt {{a^2} + {b^2}} \\\\ \\Leftrightarrow {a^2} + {b^2} = 13.\\end{array}\\)</span></p>\r\n<p><span style=\"font-size: 14pt;\">Đường tiệm cận </span><span class=\"MTConvertedEquation\">\\(y = \\frac{2}{3}x = \\frac{b}{a}x \\Rightarrow \\frac{b}{a} = \\frac{2}{3}.\\)</span></p>\r\n<p><span class=\"MTConvertedEquation\">\\( \\Leftrightarrow \\frac{a}{3} = \\frac{b}{2} \\Leftrightarrow \\frac{{{a^2}}}{9} = \\frac{{{b^2}}}{4} = \\frac{{{a^2} + {b^2}}}{{13}} = \\frac{{13}}{{13}} = 1.\\)</span></p>\r\n<p><span class=\"MTConvertedEquation\">\\( \\Rightarrow a = 3,b = 2.\\)</span></p>\r\n<p><span style=\"font-size: 14pt;\"> </span></p>\r\n<p><span class=\"mjxassistivemathml\"><span style=\"font-size: 14pt; font-family: 'Cambria Math', 'serif'; border: 1pt none windowtext; padding: 0cm;\">⇒</span></span><span style=\"font-size: 14pt;\">PTCT của hypebol</span></p>\r\n<p><span class=\"MTConvertedEquation\">\\(\\frac{{{x^2}}}{{{3^2}}} - \\frac{{{y^2}}}{{{2^2}}} = 1 \\Leftrightarrow \\frac{{{x^2}}}{9} - \\frac{{{y^2}}}{4} = 1.\\)</span></p>\r\n<p><span style=\"font-size: 14pt;\">c,</span></p>\r\n<p><span style=\"font-size: 14pt;\"> + Tâm sai của hypebol:</span><span style=\"font-size: 14.0pt;\"><span id=\"MJXc-Node-10860\" style=\"display: inline-block; border-spacing: 0px;\"><span id=\"MathJax-Element-1043-Frame\" style=\"display: inline-block; overflow-wrap: normal; max-width: none; max-height: none; min-width: 0px; min-height: 0px; float: none; word-spacing: normal;\" data-mathml=\"&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mi&gt;e&lt;/mi&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mfrac&gt;&lt;mi&gt;c&lt;/mi&gt;&lt;mi&gt;a&lt;/mi&gt;&lt;/mfrac&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;msqrt&gt;&lt;mn&gt;5&lt;/mn&gt;&lt;/msqrt&gt;&lt;mo stretchy=&quot;false&quot;&gt;&amp;#x21D2;&lt;/mo&gt;&lt;mi&gt;c&lt;/mi&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;msqrt&gt;&lt;mn&gt;5&lt;/mn&gt;&lt;/msqrt&gt;&lt;mi&gt;a&lt;/mi&gt;&lt;/math&gt;\"><span id=\"MJXc-Node-10861\" style=\"display: inline-block; box-sizing: content-box !important;\"><span id=\"MJXc-Node-10862\" style=\"display: inline-block; box-sizing: content-box !important;\"><span class=\"MTConvertedEquation\">\\(e = \\frac{c}{a} = \\sqrt 5  \\Leftrightarrow c = a\\sqrt 5  = \\sqrt {{a^2} + {b^2}} \\)</span></span></span></span></span></span></p>\r\n<p><span class=\"MTConvertedEquation\">\\( \\Leftrightarrow {a^2} + {b^2} = 5{a^2} \\Rightarrow {b^2} = 4{a^2}\\)</span><span style=\"font-size: 14.0pt;\">(1).</span></p>\r\n<p><span style=\"font-size: 14pt;\">+ </span><span style=\"font-size: 14.0pt;\">Hypebol đi qua điểm </span><span class=\"MTConvertedEquation\">\\((\\sqrt {10} ;6)\\)</span><span style=\"font-size: 14.0pt;\">nên ta có: </span><span class=\"MTConvertedEquation\">\\(\\frac{{{{(\\sqrt {10} )}^2}}}{{{a^2}}} - \\frac{{{6^2}}}{{{b^2}}} = 1\\)</span><span style=\"font-size: 14.0pt;\"> (2).</span></p>\r\n<p><span style=\"font-size: 14.0pt;\"> Thay (1) vào (2) ta có:</span></p>\r\n<p><span class=\"MTConvertedEquation\">\\(\\frac{{10}}{{{a^2}}} - \\frac{{36}}{{4{a^2}}} = 1 \\Leftrightarrow \\frac{{10}}{{{a^2}}} - \\frac{9}{{{a^2}}} = 1\\)</span></p>\r\n<p><span class=\"MTConvertedEquation\">\\( \\Leftrightarrow \\frac{1}{{{a^2}}} = 1 \\Rightarrow a = 1 \\Rightarrow {b^2} = 4 \\Rightarrow b = 2.\\)</span></p>\r\n<p><span class=\"mjxassistivemathml\"><span style=\"font-size: 14pt; font-family: 'Cambria Math', 'serif'; border: 1pt none windowtext; padding: 0cm;\">⇒</span></span><span style=\"font-size: 14pt;\">PTCT của hypebol</span></p>\r\n<p> </p>\r\n<p><span class=\"MTConvertedEquation\">\\(\\frac{{{x^2}}}{{{1^2}}} - \\frac{{{y^2}}}{{{2^2}}} = 1 \\Leftrightarrow {x^2} - \\frac{{{y^2}}}{4} = 1.\\)</span></p>\r\n<p style=\"margin: 0cm 0cm 0.0001pt; background-image: initial; background-position: initial; background-size: initial; background-repeat: initial; background-attachment: initial; background-origin: initial; background-clip: initial;\"><span style=\"font-size: 14pt;\">+ Độ dài nửa trục bằng 4 </span><span class=\"MTConvertedEquation\">\\( \\Rightarrow a = 4\\)</span><span style=\"font-size: 14.0pt;\">.</span></p>\r\n<p style=\"margin: 0cm 0cm 0.0001pt; background-image: initial; background-position: initial; background-size: initial; background-repeat: initial; background-attachment: initial; background-origin: initial; background-clip: initial;\"><span style=\"font-size: 14pt;\">+ Tiêu cự bằng<span id=\"MathJax-Element-1011-Frame\" style=\"display: inline-block; overflow-wrap: normal; max-width: none; max-height: none; min-width: 0px; min-height: 0px; float: none; word-spacing: normal;\" data-mathml=\"&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mn&gt;10&lt;/mn&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;mi&gt;c&lt;/mi&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;msqrt&gt;&lt;mrow class=&quot;MJX-TeXAtom-ORD&quot;&gt;&lt;msup&gt;&lt;mn&gt;4&lt;/mn&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;/msup&gt;&lt;/mrow&gt;&lt;mo&gt;+&lt;/mo&gt;&lt;mrow class=&quot;MJX-TeXAtom-ORD&quot;&gt;&lt;msup&gt;&lt;mi&gt;b&lt;/mi&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;/msup&gt;&lt;/mrow&gt;&lt;/msqrt&gt;&lt;mo stretchy=&quot;false&quot;&gt;&amp;#x21D2;&lt;/mo&gt;&lt;mi&gt;b&lt;/mi&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mn&gt;3&lt;/mn&gt;&lt;/math&gt;\"><span id=\"MJXc-Node-10338\" style=\"display: inline-block; border-spacing: 0px;\"><span id=\"MJXc-Node-10339\" style=\"display: inline-block; box-sizing: content-box !important;\"><span id=\"MJXc-Node-10340\" style=\"display: inline-block; box-sizing: content-box !important;\"><span class=\"MTConvertedEquation\">\\(10 = 2c = 2\\sqrt {{a^2} + {b^2}} \\)</span></span></span></span></span></span></p>\r\n<p style=\"margin: 0cm 0cm 0.0001pt 49.65pt; background-image: initial; background-position: initial; background-size: initial; background-repeat: initial; background-attachment: initial; background-origin: initial; background-clip: initial;\"><span class=\"MTConvertedEquation\">\\(\\begin{array}{l} \\Leftrightarrow 10 = 2\\sqrt {{4^2} + {b^2}} \\\\ \\Leftrightarrow \\sqrt {{4^2} + {b^2}}  = 5\\\\ \\Leftrightarrow {4^2} + {b^2} = 25\\\\ \\Leftrightarrow {b^2} = 9\\\\ \\Rightarrow b = 3.\\end{array}\\)</span></p>\r\n<p style=\"margin: 0cm 0cm 0.0001pt; background-image: initial; background-position: initial; background-size: initial; background-repeat: initial; background-attachment: initial; background-origin: initial; background-clip: initial;\"><span class=\"mjxassistivemathml\"><span id=\"MJXc-Node-10363\" style=\"display: inline-block; border-spacing: 0px;\"><span style=\"font-size: 14pt; font-family: 'Cambria Math', 'serif'; border: 1pt none windowtext; padding: 0cm;\"><span id=\"MJXc-Node-10364\" style=\"display: inline-block; box-sizing: content-box !important;\"><span id=\"MathJax-Element-1012-Frame\" style=\"display: inline-block; overflow-wrap: normal; max-width: none; max-height: none; min-width: 0px; min-height: 0px; float: none; word-spacing: normal;\" data-mathml=\"&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mo stretchy=&quot;false&quot;&gt;&amp;#x21D2;&lt;/mo&gt;&lt;/math&gt;\"><span id=\"MJXc-Node-10365\" style=\"display: inline-block; box-sizing: content-box !important;\"><span style=\"box-sizing: content-box !important;\">⇒</span></span></span></span><span style=\"font-size: 14pt;\">PTCT của hypebol<span class=\"mjx-char\"><span id=\"MJXc-Node-10366\" style=\"display: inline-block; border-spacing: 0px;\"><span style=\"border: none windowtext 1.0pt; mso-border-alt: none windowtext 0cm; padding: 0cm;\"><span id=\"MJXc-Node-10367\" style=\"display: inline-block; box-sizing: content-box !important;\"><span id=\"MathJax-Element-1013-Frame\" style=\"display: inline-block; overflow-wrap: normal; max-width: none; max-height: none; min-width: 0px; min-height: 0px; float: none; word-spacing: normal;\" data-mathml=\"&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mfrac&gt;&lt;mrow class=&quot;MJX-TeXAtom-ORD&quot;&gt;&lt;mrow class=&quot;MJX-TeXAtom-ORD&quot;&gt;&lt;msup&gt;&lt;mi&gt;x&lt;/mi&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;/msup&gt;&lt;/mrow&gt;&lt;/mrow&gt;&lt;mrow class=&quot;MJX-TeXAtom-ORD&quot;&gt;&lt;mn&gt;16&lt;/mn&gt;&lt;/mrow&gt;&lt;/mfrac&gt;&lt;mo&gt;&amp;#x2212;&lt;/mo&gt;&lt;mfrac&gt;&lt;mrow class=&quot;MJX-TeXAtom-ORD&quot;&gt;&lt;mrow class=&quot;MJX-TeXAtom-ORD&quot;&gt;&lt;msup&gt;&lt;mi&gt;y&lt;/mi&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;/msup&gt;&lt;/mrow&gt;&lt;/mrow&gt;&lt;mn&gt;9&lt;/mn&gt;&lt;/mfrac&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;/math&gt;\"><span id=\"MJXc-Node-10368\" style=\"display: inline-block; box-sizing: content-box !important;\"><span style=\"display: inline-block; box-sizing: content-box !important;\"><span style=\"box-sizing: content-box !important;\"><span id=\"MJXc-Node-10369\" style=\"display: inline-block; box-sizing: content-box !important;\"><span id=\"MJXc-Node-10370\" style=\"display: inline-block; box-sizing: content-box !important;\"><span id=\"MJXc-Node-10371\" style=\"display: inline-block; box-sizing: content-box !important;\"><span id=\"MJXc-Node-10372\" style=\"display: inline-block; box-sizing: content-box !important;\"><span id=\"MJXc-Node-10373\" style=\"display: inline-block; box-sizing: content-box !important;\"><span style=\"display: inline-block; box-sizing: content-box !important;\"><span id=\"MJXc-Node-10374\" style=\"display: inline-block; box-sizing: content-box !important;\"><span style=\"box-sizing: content-box !important;\">: </span></span></span><span class=\"MTConvertedEquation\">\\(\\frac{{{x^2}}}{{{4^2}}} - \\frac{{{y^2}}}{{{3^2}}} = 1 \\Leftrightarrow \\frac{{{x^2}}}{{16}} - \\frac{{{y^2}}}{9} = 1.\\)</span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></p>\r\n<p style=\"margin: 0cm 0cm 7.5pt; background-image: initial; background-position: initial; background-size: initial; background-repeat: initial; background-attachment: initial; background-origin: initial; background-clip: initial;\"><span style=\"font-size: 14pt;\">b)</span></p>\r\n<p style=\"margin: 0cm 0cm 0.0001pt; background-image: initial; background-position: initial; background-size: initial; background-repeat: initial; background-attachment: initial; background-origin: initial; background-clip: initial;\"><span style=\"font-size: 14pt;\">+ Tiêu cự bằng<span id=\"MathJax-Element-1014-Frame\" style=\"display: inline-block; overflow-wrap: normal; max-width: none; max-height: none; min-width: 0px; min-height: 0px; float: none; word-spacing: normal;\" data-mathml=\"&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;msqrt&gt;&lt;mn&gt;13&lt;/mn&gt;&lt;/msqrt&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;mi&gt;c&lt;/mi&gt;&lt;mo stretchy=&quot;false&quot;&gt;&amp;#x21D2;&lt;/mo&gt;&lt;mi&gt;c&lt;/mi&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;msqrt&gt;&lt;mn&gt;13&lt;/mn&gt;&lt;/msqrt&gt;&lt;/math&gt;\"><span id=\"MJXc-Node-10391\" style=\"display: inline-block; border-spacing: 0px;\"><span id=\"MJXc-Node-10392\" style=\"display: inline-block; box-sizing: content-box !important;\"><span id=\"MJXc-Node-10393\" style=\"display: inline-block; box-sizing: content-box !important;\"><span class=\"MTConvertedEquation\">\\(2\\sqrt {13}  = 2c \\Rightarrow c = \\sqrt {13} .\\)</span></span></span></span></span></span></p>\r\n<p style=\"margin: 0cm 0cm 0.0001pt; background-image: initial; background-position: initial; background-size: initial; background-repeat: initial; background-attachment: initial; background-origin: initial; background-clip: initial;\"><span style=\"font-size: 14pt;\">+ Ta có:</span><span class=\"MTConvertedEquation\">\\(2\\sqrt {13}  = 2c = 2\\sqrt {{a^2} + {b^2}} \\)</span></p>\r\n<p style=\"margin: 0cm 0cm 0.0001pt 78pt; background-image: initial; background-position: initial; background-size: initial; background-repeat: initial; background-attachment: initial; background-origin: initial; background-clip: initial;\"><span class=\"MTConvertedEquation\">\\(\\begin{array}{l} \\Leftrightarrow \\sqrt {13}  = \\sqrt {{a^2} + {b^2}} \\\\ \\Leftrightarrow {a^2} + {b^2} = 13.\\end{array}\\)</span></p>\r\n<p style=\"margin: 0cm 0cm 0.0001pt 7.1pt; background-image: initial; background-position: initial; background-size: initial; background-repeat: initial; background-attachment: initial; background-origin: initial; background-clip: initial;\"><span style=\"font-size: 14pt;\">Đường tiệm cận </span><span class=\"MTConvertedEquation\">\\(y = \\frac{2}{3}x = \\frac{b}{a}x \\Rightarrow \\frac{b}{a} = \\frac{2}{3}.\\)</span></p>\r\n<p style=\"margin: 0cm 0cm 0.0001pt 2cm; background-image: initial; background-position: initial; background-size: initial; background-repeat: initial; background-attachment: initial; background-origin: initial; background-clip: initial;\"><span class=\"MTConvertedEquation\">\\( \\Leftrightarrow \\frac{a}{3} = \\frac{b}{2} \\Leftrightarrow \\frac{{{a^2}}}{9} = \\frac{{{b^2}}}{4} = \\frac{{{a^2} + {b^2}}}{{13}} = \\frac{{13}}{{13}} = 1.\\)</span></p>\r\n<p style=\"margin: 0cm 0cm 0.0001pt 2cm; background-image: initial; background-position: initial; background-size: initial; background-repeat: initial; background-attachment: initial; background-origin: initial; background-clip: initial;\"><span class=\"MTConvertedEquation\">\\( \\Rightarrow a = 3,b = 2.\\)</span></p>\r\n<p style=\"margin: 0cm 0cm 0.0001pt 7.1pt; background-image: initial; background-position: initial; background-size: initial; background-repeat: initial; background-attachment: initial; background-origin: initial; background-clip: initial;\"><span style=\"font-size: 14pt;\"> </span></p>\r\n<p style=\"margin: 0cm 0cm 0.0001pt; background-image: initial; background-position: initial; background-size: initial; background-repeat: initial; background-attachment: initial; background-origin: initial; background-clip: initial;\"><span class=\"mjxassistivemathml\"><span style=\"font-size: 14pt; font-family: 'Cambria Math', 'serif'; border: 1pt none windowtext; padding: 0cm;\">⇒</span></span><span style=\"font-size: 14pt;\">PTCT của hypebol<span class=\"mjx-char\"><span id=\"MJXc-Node-10366\" style=\"display: inline-block; border-spacing: 0px;\"><span style=\"border: none windowtext 1.0pt; mso-border-alt: none windowtext 0cm; padding: 0cm;\"><span id=\"MJXc-Node-10367\" style=\"display: inline-block; box-sizing: content-box !important;\"><span id=\"MathJax-Element-1013-Frame\" style=\"display: inline-block; overflow-wrap: normal; max-width: none; max-height: none; min-width: 0px; min-height: 0px; float: none; word-spacing: normal;\" data-mathml=\"&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mfrac&gt;&lt;mrow class=&quot;MJX-TeXAtom-ORD&quot;&gt;&lt;mrow class=&quot;MJX-TeXAtom-ORD&quot;&gt;&lt;msup&gt;&lt;mi&gt;x&lt;/mi&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;/msup&gt;&lt;/mrow&gt;&lt;/mrow&gt;&lt;mrow class=&quot;MJX-TeXAtom-ORD&quot;&gt;&lt;mn&gt;16&lt;/mn&gt;&lt;/mrow&gt;&lt;/mfrac&gt;&lt;mo&gt;&amp;#x2212;&lt;/mo&gt;&lt;mfrac&gt;&lt;mrow class=&quot;MJX-TeXAtom-ORD&quot;&gt;&lt;mrow class=&quot;MJX-TeXAtom-ORD&quot;&gt;&lt;msup&gt;&lt;mi&gt;y&lt;/mi&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;/msup&gt;&lt;/mrow&gt;&lt;/mrow&gt;&lt;mn&gt;9&lt;/mn&gt;&lt;/mfrac&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;/math&gt;\"><span id=\"MJXc-Node-10368\" style=\"display: inline-block; box-sizing: content-box !important;\"><span style=\"display: inline-block; box-sizing: content-box !important;\"><span style=\"box-sizing: content-box !important;\"><span id=\"MJXc-Node-10369\" style=\"display: inline-block; box-sizing: content-box !important;\"><span id=\"MJXc-Node-10370\" style=\"display: inline-block; box-sizing: content-box !important;\"><span id=\"MJXc-Node-10371\" style=\"display: inline-block; box-sizing: content-box !important;\"><span id=\"MJXc-Node-10372\" style=\"display: inline-block; box-sizing: content-box !important;\"><span id=\"MJXc-Node-10373\" style=\"display: inline-block; box-sizing: content-box !important;\"><span style=\"display: inline-block; box-sizing: content-box !important;\"><span id=\"MJXc-Node-10374\" style=\"display: inline-block; box-sizing: content-box !important;\"><span style=\"box-sizing: content-box !important;\">: </span></span></span><span class=\"MTConvertedEquation\">\\(\\frac{{{x^2}}}{{{3^2}}} - \\frac{{{y^2}}}{{{2^2}}} = 1 \\Leftrightarrow \\frac{{{x^2}}}{9} - \\frac{{{y^2}}}{4} = 1.\\)</span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></p>\r\n<p><span style=\"font-size: 14pt; line-height: 115%; font-family: 'Times New Roman', 'serif';\">c,</span></p>","common_article":"","display_type":1,"vungoi_exam_id":"","article_type":1,"cmt_count":0,"zip_status":1,"last_modified_time":1683176304,"last_zip_time":1683176304,"zip_link":"https://offline.loigiaihay.com/articles/1161/122461/122461_1683176304.zip","picture":"","youtube_id":"","video_start_time":"0","quizlet_id":"0","ref_article_id":0,"readmore_display_type":0,"wiki":0,"comment_url":"https://loigiaihay.com/comment/giai-bai-39-trang-52-chuyen-de-hoc-tap-toan-10-ket-noi-tri-thuc-voi-cuoc-song-c1161a122461.html","origin_url":"https://loigiaihay.com/giai-bai-39-trang-52-chuyen-de-hoc-tap-toan-10-ket-noi-tri-thuc-voi-cuoc-song-c1161a122461.html","relate_link":[]},"callouts":[],"relate_articles":[],"others_in_cat":[{"article_id":122462,"cat_id":1161,"publish_time":1667219640,"is_link":0,"thumbnail":"","title":"Giải bài 3.10 trang 52 Chuyên đề học tập Toán 10 - Kết nối tri thức với cuộc sống","alias":"giai-bai-310-trang-52-chuyen-de-hoc-tap-toan-10-ket-noi-tri-thuc-voi-cuoc-song","introtext":"Một hypebol mà độ dài trục thực bằng độ dài trục ảo được gọi là hypebol vuông. Tìm tâm sai và phương trình hai đường tiệm cận của hypebol vuông","display_type":1,"article_type":1},{"article_id":122463,"cat_id":1161,"publish_time":1667219700,"is_link":0,"thumbnail":"","title":"Giải bài 3.11 trang 52 Chuyên đề học tập Toán 10 - Kết nối tri thức với cuộc sống","alias":"giai-bai-311-trang-52-chuyen-de-hoc-tap-toan-10-ket-noi-tri-thuc-voi-cuoc-song","introtext":"Chứng minh rằng tích các khoảng cách từ một điểm bất kì thuộc hypebol đến hai đường tiệm cận của nó là một số không đổi","display_type":1,"article_type":1},{"article_id":122464,"cat_id":1161,"publish_time":1667219760,"is_link":0,"thumbnail":"","title":"Giải bài 3.12 trang 53 Chuyên đề học tập Toán 10 - Kết nối tri thức với cuộc sống","alias":"giai-bai-312-trang-53-chuyen-de-hoc-tap-toan-10-ket-noi-tri-thuc-voi-cuoc-song","introtext":"Bốn trạm phát tín hiệu vô tuyến có vị trí A, B, C, D theo thứ tự đó thẳng hàng và cách đều với khoảng cách 200 km (H.3.16). ","display_type":1,"article_type":1},{"article_id":122460,"cat_id":1161,"publish_time":1667219520,"is_link":0,"thumbnail":"","title":"Giải bài 3.8 trang 52 Chuyên đề học tập Toán 10 - Kết nối tri thức với cuộc sống","alias":"giai-bai-38-trang-52-chuyen-de-hoc-tap-toan-10-ket-noi-tri-thuc-voi-cuoc-song","introtext":"Trong mặt phẳng tọa độ Oxy, cho hypebol có phương trình chính tắc (frac{{{x^2}}}{9} - frac{{{y^2}}}{7} = 1)","display_type":1,"article_type":1},{"article_id":122459,"cat_id":1161,"publish_time":1667219460,"is_link":0,"thumbnail":"","title":"Giải bài 3.7 trang 52 Chuyên đề học tập Toán 10 - Kết nối tri thức với cuộc sống","alias":"giai-bai-37-trang-52-chuyen-de-hoc-tap-toan-10-ket-noi-tri-thuc-voi-cuoc-song","introtext":"Trong mặt phẳng tọa độ Oxy, cho hypebol có phương trình chính tắc (frac{{{x^2}}}{9} - frac{{{y^2}}}{4} = 1)","display_type":1,"article_type":1},{"article_id":122458,"cat_id":1161,"publish_time":1667219220,"is_link":0,"thumbnail":"","title":"Giải mục 2 trang 49, 50, 51, 52 Chuyên đề học tập Toán 10 - Kết nối tri thức","alias":"giai-muc-2-trang-49-50-51-52-chuyen-de-hoc-tap-toan-10-ket-noi-tri-thuc","introtext":"Cho điểm (M({x_0};{y_0}))thuộc hypebol có hai tiêu điểm ({F_1}( - c;0),{F_2}(c;0)), độ dài trục thực bằng 2a.","display_type":2,"article_type":1},{"article_id":122457,"cat_id":1161,"publish_time":1667219040,"is_link":0,"thumbnail":"","title":"Giải mục 1 trang 47, 48, 49, 50 Chuyên đề học tập Toán 10 - Kết nối tri thức","alias":"giai-muc-1-trang-47-48-49-50-chuyen-de-hoc-tap-toan-10-ket-noi-tri-thuc","introtext":"Trong mặt phẳng tọa độ, cho hypebol có phương trình chính tắc ","display_type":2,"article_type":1}],"event_info":{"title":"Bài 6. Hypebol Chuyên đề học tập Toán 10 kết nối tri thức","cat_id":1161,"alias":"bai-6-hypebol-chuyen-de-hoc-tap-toan-10-ket-noi-tri-thuc","introtext":"","type":"event","item_id":28813,"item_type":2},"banner":[],"top_banner":"","content_expanded":[],"child_events":[{"id":"28813","title":"Bài 6. Hypebol Chuyên đề học tập Toán 10 kết nối tri thức","short_title":"Bài 6. Hypebol","alias":"bai-6-hypebol-chuyen-de-hoc-tap-toan-10-ket-noi-tri-thuc","picture":"","is_link":"0","links":"","is_hot":"0","is_all":"0","category_id":"1161","ordering":"28813","parent_id":"28811"}],"parent_events":[{"id":"28811","title":"Chuyên đề 3: Ba đường conic và ứng dụng ","short_title":"Chuyên đề 3: Ba đường conic và ứng dụng ","alias":"chuyen-de-3-ba-duong-conic-va-ung-dung","picture":"","is_link":"0","links":"","is_hot":"0","is_all":"0","category_id":"1161","ordering":"28811"}],"cfg_info":{"last_cfg_time":"1521866679","ad.popup_frequency":"0","ad.adsense.detail_bottom.unit_id":"ca-app-pub-8529835372050931/9927553003","ad.adsense.popup.unit_id":"ca-app-pub-8529835372050931/2161779402","current.force.update.version":"181","support.email":"loigiaihay.com@gmail.com","support.fanpage":"https://www.facebook.com/Loigiaihay/","popup_rating_after":"86400","admob.app_id":"ca-app-pub-8529835372050931~4358271409","admob.unit.article_detail_bottom":"ca-app-pub-8529835372050931/1883637630","admob.unit.article_detail_top":"ca-app-pub-8529835372050931/8604898230","admob.unit.event_article_top":"ca-app-pub-8529835372050931/7406887709","admob.unit.interestial":"ca-app-pub-8529835372050931/2741937409","ios_appstore_link":"https://itunes.apple.com/us/app/loigiaihay/id1209891610?mt=8","android_appstore_link":"https://play.google.com/store/apps/details?id=com.tp.loigiaihay","min_version":"2.1.3","latest_version":"1.3.9","force_update":false},"popup_ads":[]}