{"id":6844,"date":"2021-10-21T19:48:12","date_gmt":"2021-10-21T14:18:12","guid":{"rendered":"https:\/\/mathemerize.com\/?p=6844"},"modified":"2021-10-25T01:13:44","modified_gmt":"2021-10-24T19:43:44","slug":"find-the-equation-of-the-tangents-to-the-parabola-y2-9x-which-go-through-the-point-410","status":"publish","type":"post","link":"https:\/\/mathemerize.com\/find-the-equation-of-the-tangents-to-the-parabola-y2-9x-which-go-through-the-point-410\/","title":{"rendered":"Find the equation of the tangents to the parabola \\(y^2\\) = 9x which go through the point (4,10)."},"content":{"rendered":"

Solution :<\/h2>\n

Equation of tangent to the parabola \\(y^2\\) = 9x is<\/p>\n

y = mx + \\(9\\over 4m\\)<\/p>\n

Since it passes through (4,10)<\/p>\n

\\(\\therefore\\)\u00a0 10 = 4m + \\(9\\over 4m\\) \\(\\implies\\) 16\\(m^2\\) – 40m + 9 = 0<\/p>\n

m = \\(1\\over 4\\), \\(9\\over 4\\)<\/p>\n

\\(\\therefore\\) Equation of tangent’s are y = \\(x\\over 4\\) + 9 &amp; y = \\(9x\\over 4\\) + 1<\/p>\n

\n

Similar Questions<\/h3>\n

The slope of the line touching both the parabolas \\(y^2\\) = 4x and \\(x^2\\) = -32 is<\/a><\/p>\n

Find the locus of middle point of the chord of the parabola \\(y^2\\) = 4ax which pass through a given (p, q).<\/a><\/p>\n

The sum of the slopes of the tangent of the parabola \\(y^2\\)=4ax drawn from the point (2,3) is<\/a><\/p>\n

Find the value of k for which the point (k-1, k) lies inside the parabola \\(y^2\\) = 4x.<\/a><\/p>\n

The length of latus rectum of a parabola, whose focus is (2, 3) and directrix is the line x \u2013 4y + 3 = 0 is<\/a><\/p>\n","protected":false},"excerpt":{"rendered":"

Solution : Equation of tangent to the parabola \\(y^2\\) = 9x is y = mx + \\(9\\over 4m\\) Since it passes through (4,10) \\(\\therefore\\)\u00a0 10 = 4m + \\(9\\over 4m\\) \\(\\implies\\) 16\\(m^2\\) – 40m + 9 = 0 m = \\(1\\over 4\\), \\(9\\over 4\\) \\(\\therefore\\) Equation of tangent’s are y = \\(x\\over 4\\) + 9 …<\/p>\n

Find the equation of the tangents to the parabola \\(y^2\\) = 9x which go through the point (4,10).<\/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":[43,46],"tags":[],"yoast_head":"\nFind the equation of the tangents to the parabola \\(y^2\\) = 9x which go through the point (4,10).<\/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-parabola-y2-9x-which-go-through-the-point-410\/\" \/>\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 parabola \\(y^2\\) = 9x which go through the point (4,10).\" \/>\n<meta property=\"og:description\" content=\"Solution : Equation of tangent to the parabola (y^2) = 9x is y = mx + (9over 4m) Since it passes through (4,10) (therefore)\u00a0 10 = 4m + (9over 4m) (implies) 16(m^2) – 40m + 9 = 0 m = (1over 4), (9over 4) (therefore) Equation of tangent’s are y = (xover 4) + 9 … Find the equation of the tangents to the parabola (y^2) = 9x which go through the point (4,10). 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