{"id":6846,"date":"2021-10-21T19:49:34","date_gmt":"2021-10-21T14:19:34","guid":{"rendered":"https:\/\/mathemerize.com\/?p=6846"},"modified":"2021-10-25T01:13:19","modified_gmt":"2021-10-24T19:43:19","slug":"find-the-locus-of-middle-point-of-the-chord-of-the-parabola-y2-4ax-which-pass-through-a-given-p-q","status":"publish","type":"post","link":"https:\/\/mathemerize.com\/find-the-locus-of-middle-point-of-the-chord-of-the-parabola-y2-4ax-which-pass-through-a-given-p-q\/","title":{"rendered":"Find the locus of middle point of the chord of the parabola \\(y^2\\) = 4ax which pass through a given (p, q)."},"content":{"rendered":"

Solution :<\/h2>\n

Let P(h,k) be the mid point of chord of the parabola \\(y^2\\) = 4ax,<\/p>\n

so equation of chord is yk – 2a(x+h) = \\(k^2\\) – 4ah.<\/p>\n

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

\\(\\therefore\\)\u00a0 qk – 2a(p+h) = \\(k^2\\) – 4ah<\/p>\n

\\(\\therefore\\) Required locus is \\(y^2\\) – 2ax – qy + 2ap = 0<\/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

What is the equation of tangent to the parabola having slope m?<\/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 : Let P(h,k) be the mid point of chord of the parabola \\(y^2\\) = 4ax, so equation of chord is yk – 2a(x+h) = \\(k^2\\) – 4ah. Since it passes through (p,q) \\(\\therefore\\)\u00a0 qk – 2a(p+h) = \\(k^2\\) – 4ah \\(\\therefore\\) Required locus is \\(y^2\\) – 2ax – qy + 2ap = 0 Similar …<\/p>\n

Find the locus of middle point of the chord of the parabola \\(y^2\\) = 4ax which pass through a given (p, q).<\/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 locus of middle point of the chord of the parabola \\(y^2\\) = 4ax which pass through a given (p, q).<\/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-locus-of-middle-point-of-the-chord-of-the-parabola-y2-4ax-which-pass-through-a-given-p-q\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Find the locus of middle point of the chord of the parabola \\(y^2\\) = 4ax which pass through a given (p, q).\" \/>\n<meta property=\"og:description\" content=\"Solution : Let P(h,k) be the mid point of chord of the parabola (y^2) = 4ax, so equation of chord is yk – 2a(x+h) = (k^2) – 4ah. Since it passes through (p,q) (therefore)\u00a0 qk – 2a(p+h) = (k^2) – 4ah (therefore) Required locus is (y^2) – 2ax – qy + 2ap = 0 Similar … Find the locus of middle point of the chord of the parabola (y^2) = 4ax which pass through a given (p, q). 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