{"id":7046,"date":"2021-10-22T15:52:11","date_gmt":"2021-10-22T10:22:11","guid":{"rendered":"https:\/\/mathemerize.com\/?p=7046"},"modified":"2021-10-25T01:10:21","modified_gmt":"2021-10-24T19:40:21","slug":"the-sum-of-the-slopes-of-the-tangent-of-the-parabola-y24ax-drawn-from-the-point-23-is","status":"publish","type":"post","link":"https:\/\/mathemerize.com\/the-sum-of-the-slopes-of-the-tangent-of-the-parabola-y24ax-drawn-from-the-point-23-is\/","title":{"rendered":"The sum of the slopes of the tangent of the parabola \\(y^2\\)=4ax drawn from the point (2,3) is"},"content":{"rendered":"

Solution :<\/h2>\n

The equation of tangent to the parabola \\(y^2\\) = 4ax is y = mx + \\(a\\over m\\).<\/p>\n

Since it is drawn from point (2,3)<\/p>\n

Therefore it lies on tangent y = mx + \\(a\\over m\\).<\/p>\n

\\(\\implies\\) 3 = 2m + \\(a\\over m\\)<\/p>\n

\\(\\implies\\) 3m = 2\\(m^2\\) + a<\/p>\n

\\(\\implies\\)\u00a0 2\\(m^2\\) – 3m + a = 0<\/p>\n

Now, Sum of slopes is \\(3\\over 2\\).\u00a0 \u00a0 \u00a0 \u00a0[\u00a0 \\(\\because\\) sum of roots = \\(-b\\over a\\) ]<\/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

Find the equation of the tangents to the parabola \\(y^2\\) = 9x which go through the point (4,10).<\/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 : The equation of tangent to the parabola \\(y^2\\) = 4ax is y = mx + \\(a\\over m\\). Since it is drawn from point (2,3) Therefore it lies on tangent y = mx + \\(a\\over m\\). \\(\\implies\\) 3 = 2m + \\(a\\over m\\) \\(\\implies\\) 3m = 2\\(m^2\\) + a \\(\\implies\\)\u00a0 2\\(m^2\\) – 3m + …<\/p>\n

The sum of the slopes of the tangent of the parabola \\(y^2\\)=4ax drawn from the point (2,3) 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":[43,46],"tags":[],"yoast_head":"\nThe sum of the slopes of the tangent of the parabola \\(y^2\\)=4ax drawn from the point (2,3) is<\/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\/the-sum-of-the-slopes-of-the-tangent-of-the-parabola-y24ax-drawn-from-the-point-23-is\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"The sum of the slopes of the tangent of the parabola \\(y^2\\)=4ax drawn from the point (2,3) is\" \/>\n<meta property=\"og:description\" content=\"Solution : The equation of tangent to the parabola (y^2) = 4ax is y = mx + (aover m). 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(implies) 3 = 2m + (aover m) (implies) 3m = 2(m^2) + a (implies)\u00a0 2(m^2) – 3m + … The sum of the slopes of the tangent of the parabola (y^2)=4ax drawn from the point (2,3) is Read More »\" \/>\n<meta property=\"og:url\" content=\"https:\/\/mathemerize.com\/the-sum-of-the-slopes-of-the-tangent-of-the-parabola-y24ax-drawn-from-the-point-23-is\/\" \/>\n<meta property=\"og:site_name\" content=\"Mathemerize\" \/>\n<meta property=\"article:published_time\" content=\"2021-10-22T10:22:11+00:00\" \/>\n<meta property=\"article:modified_time\" content=\"2021-10-24T19:40:21+00:00\" \/>\n<meta name=\"author\" content=\"mathemerize\" \/>\n<meta name=\"twitter:card\" content=\"summary_large_image\" \/>\n<meta name=\"twitter:label1\" content=\"Written by\" \/>\n\t<meta name=\"twitter:data1\" content=\"mathemerize\" \/>\n\t<meta name=\"twitter:label2\" content=\"Est. reading time\" \/>\n\t<meta name=\"twitter:data2\" content=\"1 minute\" \/>\n<script type=\"application\/ld+json\" class=\"yoast-schema-graph\">{\"@context\":\"https:\/\/schema.org\",\"@graph\":[{\"@type\":\"Article\",\"@id\":\"https:\/\/mathemerize.com\/the-sum-of-the-slopes-of-the-tangent-of-the-parabola-y24ax-drawn-from-the-point-23-is\/#article\",\"isPartOf\":{\"@id\":\"https:\/\/mathemerize.com\/the-sum-of-the-slopes-of-the-tangent-of-the-parabola-y24ax-drawn-from-the-point-23-is\/\"},\"author\":{\"name\":\"mathemerize\",\"@id\":\"https:\/\/mathemerize.com\/#\/schema\/person\/104c8bc54f90618130a6665299bc55df\"},\"headline\":\"The sum of the slopes of the tangent of the parabola \\\\(y^2\\\\)=4ax drawn from the point (2,3) is\",\"datePublished\":\"2021-10-22T10:22:11+00:00\",\"dateModified\":\"2021-10-24T19:40:21+00:00\",\"mainEntityOfPage\":{\"@id\":\"https:\/\/mathemerize.com\/the-sum-of-the-slopes-of-the-tangent-of-the-parabola-y24ax-drawn-from-the-point-23-is\/\"},\"wordCount\":167,\"commentCount\":0,\"publisher\":{\"@id\":\"https:\/\/mathemerize.com\/#organization\"},\"articleSection\":[\"Maths Questions\",\"Parabola Questions\"],\"inLanguage\":\"en-US\",\"potentialAction\":[{\"@type\":\"CommentAction\",\"name\":\"Comment\",\"target\":[\"https:\/\/mathemerize.com\/the-sum-of-the-slopes-of-the-tangent-of-the-parabola-y24ax-drawn-from-the-point-23-is\/#respond\"]}]},{\"@type\":\"WebPage\",\"@id\":\"https:\/\/mathemerize.com\/the-sum-of-the-slopes-of-the-tangent-of-the-parabola-y24ax-drawn-from-the-point-23-is\/\",\"url\":\"https:\/\/mathemerize.com\/the-sum-of-the-slopes-of-the-tangent-of-the-parabola-y24ax-drawn-from-the-point-23-is\/\",\"name\":\"The sum of the slopes of the tangent of the parabola \\\\(y^2\\\\)=4ax drawn from the point (2,3) is\",\"isPartOf\":{\"@id\":\"https:\/\/mathemerize.com\/#website\"},\"datePublished\":\"2021-10-22T10:22:11+00:00\",\"dateModified\":\"2021-10-24T19:40:21+00:00\",\"breadcrumb\":{\"@id\":\"https:\/\/mathemerize.com\/the-sum-of-the-slopes-of-the-tangent-of-the-parabola-y24ax-drawn-from-the-point-23-is\/#breadcrumb\"},\"inLanguage\":\"en-US\",\"potentialAction\":[{\"@type\":\"ReadAction\",\"target\":[\"https:\/\/mathemerize.com\/the-sum-of-the-slopes-of-the-tangent-of-the-parabola-y24ax-drawn-from-the-point-23-is\/\"]}]},{\"@type\":\"BreadcrumbList\",\"@id\":\"https:\/\/mathemerize.com\/the-sum-of-the-slopes-of-the-tangent-of-the-parabola-y24ax-drawn-from-the-point-23-is\/#breadcrumb\",\"itemListElement\":[{\"@type\":\"ListItem\",\"position\":1,\"name\":\"Home\",\"item\":\"https:\/\/mathemerize.com\/\"},{\"@type\":\"ListItem\",\"position\":2,\"name\":\"The sum of the slopes of the tangent of the parabola \\\\(y^2\\\\)=4ax drawn from the point (2,3) is\"}]},{\"@type\":\"WebSite\",\"@id\":\"https:\/\/mathemerize.com\/#website\",\"url\":\"https:\/\/mathemerize.com\/\",\"name\":\"Mathemerize\",\"description\":\"Maths Tutorials - 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