{"id":7987,"date":"2021-11-11T23:40:37","date_gmt":"2021-11-11T18:10:37","guid":{"rendered":"https:\/\/mathemerize.com\/?p=7987"},"modified":"2021-11-11T23:44:03","modified_gmt":"2021-11-11T18:14:03","slug":"the-focal-distance-of-a-point-on-the-parabola-y2-12x-is-4-find-the-abscissa-of-this-point","status":"publish","type":"post","link":"https:\/\/mathemerize.com\/the-focal-distance-of-a-point-on-the-parabola-y2-12x-is-4-find-the-abscissa-of-this-point\/","title":{"rendered":"The focal distance of a point on the parabola \\(y^2\\) = 12x is 4. Find the abscissa of this point."},"content":{"rendered":"

Solution :<\/h2>\n

The given parabola is of form \\(y^2\\) = 4ax. On comparing, we have 4a = 12 i.e a = 3.<\/p>\n

We know that the focal distance of any point (x, y) on \\(y^2\\) = 4ax is x + a.<\/p>\n

Let the given point on the parabola \\(y^2\\) = 12 x be (x, y). Then its focal distance be x + 3.<\/p>\n

\\(\\therefore\\)\u00a0 \u00a0x + 3 = 4 \\(\\implies\\)\u00a0 x = 1.<\/p>\n

Hence, the abscissa of the given point is 1.<\/p>\n

\n

Similar Questions<\/h3>\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

What is the equation of common tangent to the parabola \\(y^2\\) = 4ax and \\(x^2\\) = 4ay ?<\/a><\/p>\n

What is the equation of tangent to the parabola having slope m?<\/a><\/p>\n","protected":false},"excerpt":{"rendered":"

Solution : The given parabola is of form \\(y^2\\) = 4ax. On comparing, we have 4a = 12 i.e a = 3. We know that the focal distance of any point (x, y) on \\(y^2\\) = 4ax is x + a. Let the given point on the parabola \\(y^2\\) = 12 x be (x, y). …<\/p>\n

The focal distance of a point on the parabola \\(y^2\\) = 12x is 4. Find the abscissa of this point.<\/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":"","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 focal distance of a point on the parabola \\(y^2\\) = 12x is 4. 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