{"id":6017,"date":"2021-10-04T22:35:17","date_gmt":"2021-10-04T17:05:17","guid":{"rendered":"https:\/\/mathemerize.com\/?p=6017"},"modified":"2021-10-04T22:48:06","modified_gmt":"2021-10-04T17:18:06","slug":"parabola-examples","status":"publish","type":"post","link":"https:\/\/mathemerize.com\/parabola-examples\/","title":{"rendered":"Parabola Examples"},"content":{"rendered":"

Here you will learn some parabola examples for better understanding of parabola concepts<\/a><\/span>.<\/p>\n\n\n

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\n\n

Example 1 : <\/span> The length of latus rectum of a parabola, whose focus is (2, 3) and directrix is the line x – 4y + 3 = 0 is –<\/p>\n

Solution : <\/span>The length of latus rectum = 2 x perp. from focus to the dirctrix

\n = 2 x |\\({2-4(3)+3}\\over {\\sqrt{1+16}}\\)| = \\(14\\over \\sqrt{17}\\)<\/p>\n


\n\n \n

Example 2 : <\/span> Find the value of k for which the point (k-1, k) lies inside the parabola \\(y^2\\) = 4x.<\/p>\n

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

\\(\\therefore\\)     \\({y_1}^2 – 4ax_1\\) < 0

\\(\\implies\\)     \\(k^2\\) – 4(k-1) < 0

\\(\\implies\\)     \\(k^2\\) – 4k + 4 < 0

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


\n\n \n

Example 3 : <\/span> Find the equation of the tangents to the parabola \\(y^2\\) = 9x which go through the point (4,10).<\/p>\n

Solution : <\/span>Equation of tangent to the parabola \\(y^2\\) = 9x is

y = mx + \\(9\\over 4m\\)

Since it passes through (4,10)

\\(\\therefore\\)     10 = 4m + \\(9\\over 4m\\) \\(\\implies\\) 16\\(m^2\\) – 40m + 9 = 0

m = \\(1\\over 4\\), \\(9\\over 4\\)

\\(\\therefore\\)     Equation of tangent’s are y = \\(x\\over 4\\) + 9 & y = \\(9x\\over 4\\) + 1<\/p>\n


\n\n \n

Example 4 : <\/span> Find the locus of middle point of the chord of the parabola \\(y^2\\) = 4ax which pass through a given (p,q).<\/p>\n

Solution : <\/span>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\\)     qk – 2a(p+h) = \\(k^2\\) – 4ah

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

Practice these given parabola examples to test your knowledge on concepts of parabola.<\/p>\n \n <\/div>\n <\/div>\n","protected":false},"excerpt":{"rendered":"

Here you will learn some parabola examples for better understanding of parabola concepts. Example 1 : The length of latus rectum of a parabola, whose focus is (2, 3) and directrix is the line x – 4y + 3 = 0 is – Solution : The length of latus rectum = 2 x perp. from …<\/p>\n

Parabola Examples<\/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":[12],"tags":[],"yoast_head":"\nParabola Examples - Mathemerize<\/title>\n<meta name=\"description\" content=\"Solve these Parabola examples to practice and test your knowledge of Parabola concepts.\" \/>\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\/parabola-examples\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Parabola Examples - 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