{"id":6782,"date":"2021-10-21T16:42:59","date_gmt":"2021-10-21T11:12:59","guid":{"rendered":"https:\/\/mathemerize.com\/?p=6782"},"modified":"2021-10-23T17:12:06","modified_gmt":"2021-10-23T11:42:06","slug":"find-the-equation-of-ellipse-whose-foci-are-2-3-2-3-and-whose-semi-major-axis-is-of-length-sqrt5","status":"publish","type":"post","link":"https:\/\/mathemerize.com\/find-the-equation-of-ellipse-whose-foci-are-2-3-2-3-and-whose-semi-major-axis-is-of-length-sqrt5\/","title":{"rendered":"Find the equation of ellipse whose foci are (2, 3), (-2, 3) and whose semi major axis is of length \\(\\sqrt{5}\\)."},"content":{"rendered":"<h2>Solution :<\/h2>\n<p>Here S = (2, 3) &amp; S&#8217; is (-2, 3) and b = \\(\\sqrt{5}\\) \\(\\implies\\) SS&#8217; = 4 = 2ae \\(\\implies\\) ae = 2<\/p>\n<p>but \\(b^2\\) = \\(a^2(1-e^2)\\) \\(\\implies\\) 5 = \\(a^2\\) &#8211; 4 \\(\\implies\\) a = 3<\/p>\n<p>Hence the equation to major axis is y = 3.<\/p>\n<p>Centre of ellipse is midpoint of SS&#8217; i.e. (0, 3)<\/p>\n<p>\\(\\therefore\\) Equation to ellipse is \\(x^2\\over a^2\\) + \\({(y-3)}^2\\over b^2\\) = 1 or \\(x^2\\over 9\\) + \\({(y-3)}^2\\over 5\\) = 1<\/p>\n<hr \/>\n<h3 style=\"text-align: center;\">Similar Questions<\/h3>\n<p><a class=\"row-title\" href=\"https:\/\/mathemerize.com\/the-foci-of-an-ellipse-are-pm-2-0-and-its-eccentricity-is-1-2-find-its-equation\/\" aria-label=\"\u201cThe foci of an ellipse are \\((\\pm 2, 0)\\) and its eccentricity is 1\/2, find its equation.\u201d (Edit)\">The foci of an ellipse are \\((\\pm 2, 0)\\) and its eccentricity is 1\/2, find its equation.<\/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<p><a class=\"row-title\" href=\"https:\/\/mathemerize.com\/find-the-equation-of-the-ellipse-whose-axes-are-along-the-coordinate-axes-vertices-are-0-pm-10-and-eccentricity-e-4-5\/\" aria-label=\"\u201cFind the equation of the ellipse whose axes are along the coordinate axes, vertices are \\((0, \\pm 10)\\) and eccentricity e = 4\/5.\u201d (Edit)\">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<p><a class=\"row-title\" href=\"https:\/\/mathemerize.com\/find-the-equation-of-the-tangents-to-the-ellipse-3x24y2-12-which-are-perpendicular-to-the-line-y-2x-4\/\" aria-label=\"\u201cFind the equation of the tangents to the ellipse \\(3x^2+4y^2\\) = 12 which are perpendicular to the line y + 2x = 4.\u201d (Edit)\">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<p><a class=\"row-title\" href=\"https:\/\/mathemerize.com\/for-what-value-of-k-does-the-line-y-x-k-touches-the-ellipse-9x2-16y2-144\/\" aria-label=\"\u201cFor what value of k does the line y = x + k touches the ellipse \\(9x^2 + 16y^2\\) = 144.\u201d (Edit)\">For what value of k does the line y = x + k touches the ellipse \\(9x^2 + 16y^2\\) = 144.<\/a><\/p>\n\n\n<p><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Solution : Here S = (2, 3) &amp; S&#8217; is (-2, 3) and b = \\(\\sqrt{5}\\) \\(\\implies\\) SS&#8217; = 4 = 2ae \\(\\implies\\) ae = 2 but \\(b^2\\) = \\(a^2(1-e^2)\\) \\(\\implies\\) 5 = \\(a^2\\) &#8211; 4 \\(\\implies\\) a = 3 Hence the equation to major axis is y = 3. Centre of ellipse is midpoint &hellip;<\/p>\n<p class=\"read-more\"> <a class=\"\" href=\"https:\/\/mathemerize.com\/find-the-equation-of-ellipse-whose-foci-are-2-3-2-3-and-whose-semi-major-axis-is-of-length-sqrt5\/\"> <span class=\"screen-reader-text\">Find the equation of ellipse whose foci are (2, 3), (-2, 3) and whose semi major axis is of length \\(\\sqrt{5}\\).<\/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":[49,43],"tags":[],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v20.12 - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>Find the equation of ellipse whose foci are (2, 3), (-2, 3) and whose semi major axis is of length \\(\\sqrt{5}\\).<\/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-ellipse-whose-foci-are-2-3-2-3-and-whose-semi-major-axis-is-of-length-sqrt5\/\" \/>\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 ellipse whose foci are (2, 3), (-2, 3) and whose semi major axis is of length \\(\\sqrt{5}\\).\" \/>\n<meta property=\"og:description\" content=\"Solution : Here S = (2, 3) &amp; S&#8217; is (-2, 3) and b = (sqrt{5}) (implies) SS&#8217; = 4 = 2ae (implies) ae = 2 but (b^2) = (a^2(1-e^2)) (implies) 5 = (a^2) &#8211; 4 (implies) a = 3 Hence the equation to major axis is y = 3. Centre of ellipse is midpoint &hellip; Find the equation of ellipse whose foci are (2, 3), (-2, 3) and whose semi major axis is of length (sqrt{5}). 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Centre of ellipse is midpoint &hellip; Find the equation of ellipse whose foci are (2, 3), (-2, 3) and whose semi major axis is of length (sqrt{5}). 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