{"id":6799,"date":"2021-10-21T17:15:52","date_gmt":"2021-10-21T11:45:52","guid":{"rendered":"https:\/\/mathemerize.com\/?p=6799"},"modified":"2021-10-23T17:04:47","modified_gmt":"2021-10-23T11:34:47","slug":"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","status":"publish","type":"post","link":"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\/","title":{"rendered":"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 :"},"content":{"rendered":"

Solution :<\/h2>\n

For ellipse e = \\(4\\over 5\\), so foci = (\\(\\pm\\)4, 0)<\/p>\n

for hyperbola e = 2, so a = \\(ae\\over e\\) = \\(4\\over 2\\) = 2, b = \\(2\\sqrt{4-1}\\) = 2\\(\\sqrt{3}\\)<\/p>\n

Hence the equation of the hyperbola is \\(x^2\\over 4\\) – \\(y^2\\over 12\\) = 1<\/p>\n

\n

Similar Questions<\/h3>\n

Find the equation of the ellipse whose axes are along the coordinate axes, vertices are \\((0, \\pm 10)\\) and eccentricity e = 4\/5.<\/a><\/p>\n

The foci of an ellipse are \\((\\pm 2, 0)\\) and its eccentricity is 1\/2, find its equation.<\/a><\/p>\n

Find the equation of the tangents to the ellipse \\(3x^2+4y^2\\) = 12 which are perpendicular to the line y + 2x = 4.<\/a><\/p>\n

For what value of k does the line y = x + k touches the ellipse \\(9x^2 + 16y^2\\) = 144.<\/a><\/p>\n

Find the equation of ellipse whose foci are (2, 3), (-2, 3) and whose semi major axis is of length \\(\\sqrt{5}\\).<\/a><\/p>\n","protected":false},"excerpt":{"rendered":"

Solution : For ellipse e = \\(4\\over 5\\), so foci = (\\(\\pm\\)4, 0) for hyperbola e = 2, so a = \\(ae\\over e\\) = \\(4\\over 2\\) = 2, b = \\(2\\sqrt{4-1}\\) = 2\\(\\sqrt{3}\\) Hence the equation of the hyperbola is \\(x^2\\over 4\\) – \\(y^2\\over 12\\) = 1 Similar Questions Find the equation of the ellipse …<\/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 :<\/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":[49,51,43],"tags":[],"yoast_head":"\nIf the foci of a hyperbola are foci of the ellipse \\(x^2\\over 25\\) + \\(y^2\\over 9\\) = 1. 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