{"id":6784,"date":"2021-10-21T16:45:03","date_gmt":"2021-10-21T11:15:03","guid":{"rendered":"https:\/\/mathemerize.com\/?p=6784"},"modified":"2021-10-23T17:11:42","modified_gmt":"2021-10-23T11:41:42","slug":"for-what-value-of-k-does-the-line-y-x-k-touches-the-ellipse-9x2-16y2-144","status":"publish","type":"post","link":"https:\/\/mathemerize.com\/for-what-value-of-k-does-the-line-y-x-k-touches-the-ellipse-9x2-16y2-144\/","title":{"rendered":"For what value of k does the line y = x + k touches the ellipse \\(9x^2 + 16y^2\\) = 144."},"content":{"rendered":"<h2>Solution :<\/h2>\n<p>\\(\\because\\) Equation of ellipse is \\(9x^2 + 16y^2\\) = 144 or \\(x^2\\over 16\\) + \\({(y-3)}^2\\over 9\\) = 1<\/p>\n<p>comparing this with \\(x^2\\over a^2\\) + \\(y^2\\over b^2\\) = 1 then we get \\(a^2\\) = 16 and \\(b^2\\) = 9<\/p>\n<p>and comparing the line y = x + k with y = mx + c ; m = 1 and c = k<\/p>\n<p>If the line y = x + k touches the ellipse \\(9x^2 + 16y^2\\) = 144, then \\(c^2\\) = \\(a^2m^2 + b^2\\)<\/p>\n<p>\\(\\implies\\) \\(k^2\\) = 16 \\(\\times\\) \\(1^2\\) + 9 \\(\\implies\\) \\(k^2\\) = 25<\/p>\n<p>\\(\\therefore\\)\u00a0 k = \\(\\pm\\)5<\/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\/find-the-equation-of-ellipse-whose-foci-are-2-3-2-3-and-whose-semi-major-axis-is-of-length-sqrt5\/\" aria-label=\"\u201cFind the equation of ellipse whose foci are (2, 3), (-2, 3) and whose semi major axis is of length \\(\\sqrt{5}\\).\u201d (Edit)\">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":"<p>Solution : \\(\\because\\) Equation of ellipse is \\(9x^2 + 16y^2\\) = 144 or \\(x^2\\over 16\\) + \\({(y-3)}^2\\over 9\\) = 1 comparing this with \\(x^2\\over a^2\\) + \\(y^2\\over b^2\\) = 1 then we get \\(a^2\\) = 16 and \\(b^2\\) = 9 and comparing the line y = x + k with y = mx + c &hellip;<\/p>\n<p class=\"read-more\"> <a class=\"\" href=\"https:\/\/mathemerize.com\/for-what-value-of-k-does-the-line-y-x-k-touches-the-ellipse-9x2-16y2-144\/\"> <span class=\"screen-reader-text\">For what value of k does the line y = x + k touches the ellipse \\(9x^2 + 16y^2\\) = 144.<\/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>For what value of k does the line y = x + k touches the ellipse \\(9x^2 + 16y^2\\) = 144.<\/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\/for-what-value-of-k-does-the-line-y-x-k-touches-the-ellipse-9x2-16y2-144\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"For what value of k does the line y = x + k touches the ellipse \\(9x^2 + 16y^2\\) = 144.\" \/>\n<meta property=\"og:description\" content=\"Solution : (because) Equation of ellipse is (9x^2 + 16y^2) = 144 or (x^2over 16) + ({(y-3)}^2over 9) = 1 comparing this with (x^2over a^2) + (y^2over b^2) = 1 then we get (a^2) = 16 and (b^2) = 9 and comparing the line y = x + k with y = mx + c &hellip; For what value of k does the line y = x + k touches the ellipse (9x^2 + 16y^2) = 144. Read More &raquo;\" \/>\n<meta property=\"og:url\" content=\"https:\/\/mathemerize.com\/for-what-value-of-k-does-the-line-y-x-k-touches-the-ellipse-9x2-16y2-144\/\" \/>\n<meta property=\"og:site_name\" content=\"Mathemerize\" \/>\n<meta property=\"article:published_time\" content=\"2021-10-21T11:15:03+00:00\" \/>\n<meta property=\"article:modified_time\" content=\"2021-10-23T11:41:42+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\/for-what-value-of-k-does-the-line-y-x-k-touches-the-ellipse-9x2-16y2-144\/#article\",\"isPartOf\":{\"@id\":\"https:\/\/mathemerize.com\/for-what-value-of-k-does-the-line-y-x-k-touches-the-ellipse-9x2-16y2-144\/\"},\"author\":{\"name\":\"mathemerize\",\"@id\":\"https:\/\/mathemerize.com\/#\/schema\/person\/104c8bc54f90618130a6665299bc55df\"},\"headline\":\"For what value of k does the line y = x + k touches the ellipse \\\\(9x^2 + 16y^2\\\\) = 144.\",\"datePublished\":\"2021-10-21T11:15:03+00:00\",\"dateModified\":\"2021-10-23T11:41:42+00:00\",\"mainEntityOfPage\":{\"@id\":\"https:\/\/mathemerize.com\/for-what-value-of-k-does-the-line-y-x-k-touches-the-ellipse-9x2-16y2-144\/\"},\"wordCount\":181,\"commentCount\":0,\"publisher\":{\"@id\":\"https:\/\/mathemerize.com\/#organization\"},\"articleSection\":[\"Ellipse Questions\",\"Maths Questions\"],\"inLanguage\":\"en-US\",\"potentialAction\":[{\"@type\":\"CommentAction\",\"name\":\"Comment\",\"target\":[\"https:\/\/mathemerize.com\/for-what-value-of-k-does-the-line-y-x-k-touches-the-ellipse-9x2-16y2-144\/#respond\"]}]},{\"@type\":\"WebPage\",\"@id\":\"https:\/\/mathemerize.com\/for-what-value-of-k-does-the-line-y-x-k-touches-the-ellipse-9x2-16y2-144\/\",\"url\":\"https:\/\/mathemerize.com\/for-what-value-of-k-does-the-line-y-x-k-touches-the-ellipse-9x2-16y2-144\/\",\"name\":\"For what value of k does the line y = x + k touches the ellipse \\\\(9x^2 + 16y^2\\\\) = 144.\",\"isPartOf\":{\"@id\":\"https:\/\/mathemerize.com\/#website\"},\"datePublished\":\"2021-10-21T11:15:03+00:00\",\"dateModified\":\"2021-10-23T11:41:42+00:00\",\"breadcrumb\":{\"@id\":\"https:\/\/mathemerize.com\/for-what-value-of-k-does-the-line-y-x-k-touches-the-ellipse-9x2-16y2-144\/#breadcrumb\"},\"inLanguage\":\"en-US\",\"potentialAction\":[{\"@type\":\"ReadAction\",\"target\":[\"https:\/\/mathemerize.com\/for-what-value-of-k-does-the-line-y-x-k-touches-the-ellipse-9x2-16y2-144\/\"]}]},{\"@type\":\"BreadcrumbList\",\"@id\":\"https:\/\/mathemerize.com\/for-what-value-of-k-does-the-line-y-x-k-touches-the-ellipse-9x2-16y2-144\/#breadcrumb\",\"itemListElement\":[{\"@type\":\"ListItem\",\"position\":1,\"name\":\"Home\",\"item\":\"https:\/\/mathemerize.com\/\"},{\"@type\":\"ListItem\",\"position\":2,\"name\":\"For what value of k does the line y = x + k touches the ellipse \\\\(9x^2 + 16y^2\\\\) = 144.\"}]},{\"@type\":\"WebSite\",\"@id\":\"https:\/\/mathemerize.com\/#website\",\"url\":\"https:\/\/mathemerize.com\/\",\"name\":\"Mathemerize\",\"description\":\"Maths Tutorials - 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