{"id":6801,"date":"2021-10-21T17:19:08","date_gmt":"2021-10-21T11:49:08","guid":{"rendered":"https:\/\/mathemerize.com\/?p=6801"},"modified":"2021-10-25T00:04:24","modified_gmt":"2021-10-24T18:34:24","slug":"the-eccentricity-of-the-conjugate-hyperbola-to-the-hyperbola-x2-3y2-1-is","status":"publish","type":"post","link":"https:\/\/mathemerize.com\/the-eccentricity-of-the-conjugate-hyperbola-to-the-hyperbola-x2-3y2-1-is\/","title":{"rendered":"The eccentricity of the conjugate hyperbola to the hyperbola \\(x^2-3y^2\\) = 1 is"},"content":{"rendered":"<h2>Solution :<\/h2>\n<p>Equation of the conjugate hyperbola to the hyperbola \\(x^2-3y^2\\) = 1 is<\/p>\n<p>\\(-x^2-3y^2\\) = 1 \\(\\implies\\) \\(-x^2\\over 1\\) + \\(y^2\\over {1\/3}\\) = 1<\/p>\n<p>Here \\(a^2\\) = 1, \\(b^2\\) = \\(1\\over 3\\)<\/p>\n<p>\\(\\therefore\\)\u00a0 eccentricity e = \\(\\sqrt{1 + a^2\/b^2}\\) = \\(\\sqrt{1+3}\\) = 2<\/p>\n<hr \/>\n<h3 style=\"text-align: center;\">Similar Questions<\/h3>\n<p><a class=\"row-title\" href=\"https:\/\/mathemerize.com\/angle-between-asymptotes-of-hyperbola-xy8-is\/\" aria-label=\"\u201cAngle between asymptotes of hyperbola xy=8 is\u201d (Edit)\">Angle between asymptotes of hyperbola xy=8 is<\/a><\/p>\n<p><a class=\"row-title\" href=\"https:\/\/mathemerize.com\/find-the-asymptotes-of-the-hyperbola-2x2-5xy-2y2-4x-5y-0-find-also-the-general-equation-of-all-the-hyperbolas-having-the-same-set-of-asymptotes\/\" aria-label=\"\u201cFind the asymptotes of the hyperbola \\(2x^2 + 5xy + 2y^2 + 4x + 5y\\) = 0. Find also the general equation of all the hyperbolas having the same set of asymptotes.\u201d (Edit)\">Find the asymptotes of the hyperbola \\(2x^2 + 5xy + 2y^2 + 4x + 5y\\) = 0. Find also the general equation of all the hyperbolas having the same set of asymptotes.<\/a><\/p>\n<p><a class=\"row-title\" href=\"https:\/\/mathemerize.com\/find-the-equation-of-the-tangent-to-the-hyperbola-x2-4y2-36-which-is-perpendicular-to-the-line-x-y-4-0\/\" aria-label=\"\u201cFind the equation of the tangent to the hyperbola \\(x^2 \u2013 4y^2\\) = 36 which is perpendicular to the line x \u2013 y + 4 = 0\u201d (Edit)\">Find the equation of the tangent to the hyperbola \\(x^2 \u2013 4y^2\\) = 36 which is perpendicular to the line x \u2013 y + 4 = 0<\/a><\/p>\n<p><a class=\"row-title\" href=\"https:\/\/mathemerize.com\/find-the-normal-to-the-hyperbola-x2over-16-y2over-9-1-whose-slope-is-1\/\" aria-label=\"\u201cFind the normal to the hyperbola \\(x^2\\over 16\\) \u2013 \\(y^2\\over 9\\) = 1 whose slope is 1.\u201d (Edit)\">Find the normal to the hyperbola \\(x^2\\over 16\\) \u2013 \\(y^2\\over 9\\) = 1 whose slope is 1.<\/a><\/p>\n<p><a class=\"row-title\" href=\"https:\/\/mathemerize.com\/if-the-foci-of-a-hyperbola-are-foci-of-the-ellipse-x2over-25-y2over-9-1-if-the-eccentricity-of-the-hyperbola-be-2-then-its-equation-is\/\" aria-label=\"\u201cIf the foci of a hyperbola are foci of the ellipse \\(x^2\\over 25\\) + \\(y^2\\over 9\\) = 1. If the eccentricity of the hyperbola be 2, then its equation is :\u201d (Edit)\">If the foci of a hyperbola are foci of the ellipse \\(x^2\\over 25\\) + \\(y^2\\over 9\\) = 1. If the eccentricity of the hyperbola be 2, then its equation is :<\/a><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Solution : Equation of the conjugate hyperbola to the hyperbola \\(x^2-3y^2\\) = 1 is \\(-x^2-3y^2\\) = 1 \\(\\implies\\) \\(-x^2\\over 1\\) + \\(y^2\\over {1\/3}\\) = 1 Here \\(a^2\\) = 1, \\(b^2\\) = \\(1\\over 3\\) \\(\\therefore\\)\u00a0 eccentricity e = \\(\\sqrt{1 + a^2\/b^2}\\) = \\(\\sqrt{1+3}\\) = 2 Similar Questions Angle between asymptotes of hyperbola xy=8 is Find the &hellip;<\/p>\n<p class=\"read-more\"> <a class=\"\" href=\"https:\/\/mathemerize.com\/the-eccentricity-of-the-conjugate-hyperbola-to-the-hyperbola-x2-3y2-1-is\/\"> <span class=\"screen-reader-text\">The eccentricity of the conjugate hyperbola to the hyperbola \\(x^2-3y^2\\) = 1 is<\/span> Read More &raquo;<\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"site-sidebar-layout":"default","site-content-layout":"default","ast-global-header-display":"","ast-main-header-display":"","ast-hfb-above-header-display":"","ast-hfb-below-header-display":"","ast-hfb-mobile-header-display":"","site-post-title":"","ast-breadcrumbs-content":"","ast-featured-img":"","footer-sml-layout":"","theme-transparent-header-meta":"default","adv-header-id-meta":"","stick-header-meta":"","header-above-stick-meta":"","header-main-stick-meta":"","header-below-stick-meta":""},"categories":[51,43],"tags":[],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v20.12 - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>The eccentricity of the conjugate hyperbola to the hyperbola \\(x^2-3y^2\\) = 1 is<\/title>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, 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