{"id":6787,"date":"2021-10-21T16:47:53","date_gmt":"2021-10-21T11:17:53","guid":{"rendered":"https:\/\/mathemerize.com\/?p=6787"},"modified":"2021-10-23T17:06:42","modified_gmt":"2021-10-23T11:36:42","slug":"find-the-equation-of-the-tangents-to-the-ellipse-3x24y2-12-which-are-perpendicular-to-the-line-y-2x-4","status":"publish","type":"post","link":"https:\/\/mathemerize.com\/find-the-equation-of-the-tangents-to-the-ellipse-3x24y2-12-which-are-perpendicular-to-the-line-y-2x-4\/","title":{"rendered":"Find the equation of the tangents to the ellipse \\(3x^2+4y^2\\) = 12 which are perpendicular to the line y + 2x = 4."},"content":{"rendered":"

Solution :<\/h2>\n

Let m be the slope of the tangent, since the tangent is perpendicular to the line y + 2x = 4<\/p>\n

\\(\\therefore\\)\u00a0 mx – 2 = -1 \\(\\implies\\) m = \\(1\\over 2\\)<\/p>\n

Since \\(3x^2+4y^2\\) = 12 or \\(x^2\\over 4\\) + \\(y^2\\over 3\\) = 1<\/p>\n

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

\\(\\therefore\\) \\(a^2\\) = 4 and \\(b^2\\) = 3<\/p>\n

So the equation of the tangent are y = \\(1\\over 2\\)x \\(\\pm\\) \\(\\sqrt{4\\times {1\\over 4} + 3}\\)<\/p>\n

\\(\\implies\\) y = \\(1\\over 2\\)x \\(\\pm\\) 2 or x – 2y \\(\\pm\\) 4 = 0<\/p>\n

\n

Similar Questions<\/h3>\n

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

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

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 : Let m be the slope of the tangent, since the tangent is perpendicular to the line y + 2x = 4 \\(\\therefore\\)\u00a0 mx – 2 = -1 \\(\\implies\\) m = \\(1\\over 2\\) Since \\(3x^2+4y^2\\) = 12 or \\(x^2\\over 4\\) + \\(y^2\\over 3\\) = 1 Comparing this with \\(x^2\\over a^2\\) + \\(y^2\\over b^2\\) = …<\/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.<\/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":[49,43],"tags":[],"yoast_head":"\nFind the equation of the tangents to the ellipse \\(3x^2+4y^2\\) = 12 which are perpendicular to the line y + 2x = 4.<\/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-tangents-to-the-ellipse-3x24y2-12-which-are-perpendicular-to-the-line-y-2x-4\/\" \/>\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 tangents to the ellipse \\(3x^2+4y^2\\) = 12 which are perpendicular to the line y + 2x = 4.\" \/>\n<meta property=\"og:description\" content=\"Solution : Let m be the slope of the tangent, since the tangent is perpendicular to the line y + 2x = 4 (therefore)\u00a0 mx – 2 = -1 (implies) m = (1over 2) Since (3x^2+4y^2) = 12 or (x^2over 4) + (y^2over 3) = 1 Comparing this with (x^2over a^2) + (y^2over b^2) = … Find the equation of the tangents to the ellipse (3x^2+4y^2) = 12 which are perpendicular to the line y + 2x = 4. 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