{"id":6803,"date":"2021-10-21T17:34:08","date_gmt":"2021-10-21T12:04:08","guid":{"rendered":"https:\/\/mathemerize.com\/?p=6803"},"modified":"2021-10-25T00:04:34","modified_gmt":"2021-10-24T18:34:34","slug":"find-the-equation-of-the-tangent-to-the-hyperbola-x2-4y2-36-which-is-perpendicular-to-the-line-x-y-4-0","status":"publish","type":"post","link":"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\/","title":{"rendered":"Find the equation of the tangent to the hyperbola \\(x^2 – 4y^2\\) = 36 which is perpendicular to the line x – y + 4 = 0"},"content":{"rendered":"

Solution :<\/h2>\n

Let m be the slope of the tangent, since the tangent is perpendicular to the line x – y = 0<\/p>\n

\\(\\therefore\\)\u00a0 m\\(\\times\\)1 = -1 \\(\\implies\\) m = -1<\/p>\n

Since \\(x^2-4y^2\\) = 36 or \\(x^2\\over 36\\) – \\(y^2\\over 9\\) = 1<\/p>\n

Comparing this with \\(x^2\\over a^2\\) – \\(y^2\\over b^2\\) = 1<\/p>\n

\\(\\therefore\\); \\(a^2\\) = 36 and \\(b^2\\) = 9<\/p>\n

So the equation of the tangent are y = -1x \\(\\pm\\) \\(\\sqrt{36\\times {-1}^2 – 9}\\)<\/p>\n

\\(\\implies\\) y = x \\(\\pm\\) \\(\\sqrt{27}\\) \\(\\implies\\) x + y \\(\\pm\\) 3\\(\\sqrt{3}\\) = 0<\/p>\n

\n

Similar Questions<\/h3>\n

Angle between asymptotes of hyperbola xy=8 is<\/a><\/p>\n

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

Find the normal to the hyperbola \\(x^2\\over 16\\) \u2013 \\(y^2\\over 9\\) = 1 whose slope is 1.<\/a><\/p>\n

The eccentricity of the conjugate hyperbola to the hyperbola \\(x^2-3y^2\\) = 1 is<\/a><\/p>\n

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":"

Solution : Let m be the slope of the tangent, since the tangent is perpendicular to the line x – y = 0 \\(\\therefore\\)\u00a0 m\\(\\times\\)1 = -1 \\(\\implies\\) m = -1 Since \\(x^2-4y^2\\) = 36 or \\(x^2\\over 36\\) – \\(y^2\\over 9\\) = 1 Comparing this with \\(x^2\\over a^2\\) – \\(y^2\\over b^2\\) = 1 \\(\\therefore\\); \\(a^2\\) …<\/p>\n

Find the equation of the tangent to the hyperbola \\(x^2 – 4y^2\\) = 36 which is perpendicular to the line x – y + 4 = 0<\/span> Read More »<\/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":"\nFind the equation of the tangent to the hyperbola \\(x^2 - 4y^2\\) = 36 which is perpendicular to the line x - y + 4 = 0<\/title>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" 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\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Find the equation of the tangent to the hyperbola \\(x^2 - 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