{"id":6842,"date":"2021-10-21T19:45:47","date_gmt":"2021-10-21T14:15:47","guid":{"rendered":"https:\/\/mathemerize.com\/?p=6842"},"modified":"2021-10-25T01:14:28","modified_gmt":"2021-10-24T19:44:28","slug":"find-the-value-of-k-for-which-the-point-k-1-k-lies-inside-the-parabola-y2-4x","status":"publish","type":"post","link":"https:\/\/mathemerize.com\/find-the-value-of-k-for-which-the-point-k-1-k-lies-inside-the-parabola-y2-4x\/","title":{"rendered":"Find the value of k for which the point (k-1, k) lies inside the parabola \\(y^2\\) = 4x."},"content":{"rendered":"

Solution :<\/h2>\n

\\(\\because\\) Point (k-1, k) lies inside the parabola \\(y^2\\) = 4x.<\/p>\n

\\(\\therefore\\)\u00a0 \\({y_1}^2 – 4ax_1\\) < 0<\/p>\n

\\(\\implies\\)\u00a0 \\(k^2\\) – 4(k-1) < 0<\/p>\n

\\(\\implies\\)\u00a0 \\(k^2\\) – 4k + 4 < 0<\/p>\n

\\((k-2)^2\\) < 0 \\(\\implies\\) k \\(\\in\\) \\(\\phi\\)<\/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

What is the equation of common tangent to the parabola \\(y^2\\) = 4ax and \\(x^2\\) = 4ay ?<\/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 : \\(\\because\\) Point (k-1, k) lies inside the parabola \\(y^2\\) = 4x. \\(\\therefore\\)\u00a0 \\({y_1}^2 – 4ax_1\\) < 0 \\(\\implies\\)\u00a0 \\(k^2\\) – 4(k-1) < 0 \\(\\implies\\)\u00a0 \\(k^2\\) – 4k + 4 < 0 \\((k-2)^2\\) < 0 \\(\\implies\\) k \\(\\in\\) \\(\\phi\\) Similar Questions The slope of the line touching both the parabolas \\(y^2\\) = 4x and …<\/p>\n

Find the value of k for which the point (k-1, k) lies inside the parabola \\(y^2\\) = 4x.<\/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 value of k for which the point (k-1, k) lies inside the parabola \\(y^2\\) = 4x.<\/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-value-of-k-for-which-the-point-k-1-k-lies-inside-the-parabola-y2-4x\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Find the value of k for which the point (k-1, k) lies inside the parabola \\(y^2\\) = 4x.\" \/>\n<meta property=\"og:description\" content=\"Solution : (because) Point (k-1, k) lies inside the parabola (y^2) = 4x. (therefore)\u00a0 ({y_1}^2 – 4ax_1) < 0 (implies)\u00a0 (k^2) – 4(k-1) < 0 (implies)\u00a0 (k^2) – 4k + 4 < 0 ((k-2)^2) < 0 (implies) k (in) (phi) Similar Questions The slope of the line touching both the parabolas (y^2) = 4x and … Find the value of k for which the point (k-1, k) lies inside the parabola (y^2) = 4x. 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