{"id":10042,"date":"2022-02-15T16:11:27","date_gmt":"2022-02-15T10:41:27","guid":{"rendered":"https:\/\/mathemerize.com\/?p=10042"},"modified":"2022-02-15T22:53:40","modified_gmt":"2022-02-15T17:23:40","slug":"length-of-latus-rectum-of-parabola-formula","status":"publish","type":"post","link":"https:\/\/mathemerize.com\/length-of-latus-rectum-of-parabola-formula\/","title":{"rendered":"Length of Latus Rectum of Parabola Formula"},"content":{"rendered":"

Here you will learn formula to find the length of latus rectum of parabola with examples.<\/p>\n

Let’s begin –<\/p>\n

Latus Rectum of Parabola<\/h2>\n

A double ordinate through the focus is called the latus rectum i.e. the latus rectum of a parabola<\/strong> is a chord passing through the focus perpendicular to the axis.<\/p><\/blockquote>\n

In the given figure, LSL’ is the latus rectum of the parabola \\(y^2\\) = 4ax.\"parabola\"<\/p>\n

By the symmetry of the curve SL = SL’ = \\(\\lambda\\) (say). So, the coordinates of L are \\((a, \\lambda)\\).<\/p>\n

Since L lies on \\(y^2\\) = 4ax, therefore<\/p>\n

\\({\\lambda}^2\\) = \\(4a^2\\)  \\(\\implies\\)  \\(\\lambda\\) = 2a<\/p>\n

\\(\\implies\\)  LL’ = \\(2\\lambda\\) = 4a<\/p>\n

Hence, Latus Rectum<\/strong> = 4a<\/p>\n

Note<\/strong> : The length of latus rectum<\/strong> of all other forms of parabola i.e. \\(x^2\\) = 4ay , \\(y^2\\) = -4ax and \\(x^2\\) = -4ay<\/strong> is also equal to 4a<\/strong>.<\/p>\n

Also Read<\/strong> : Different Types of Parabola Equations<\/a><\/p>\n

Coordinates of Latus Rectum<\/h2>\n

The coordinates of L and L’<\/strong> , end points of the latus rectum, are (a, 2a) and (a, -2a)<\/strong> respectively.<\/p><\/blockquote>\n

Example<\/span><\/strong> : For the given parabola, find the length of the latus rectum:<\/p>\n

(i) \\(y^2\\) = 8x<\/p>\n

(ii) \\(x^2\\) = -16y<\/p>\n

Solution<\/strong><\/span> :<\/p>\n

(i) The given parabola is of the form \\(y^2\\) = 4ax, where 4a = 8 i.e. a = 2.<\/p>\n

Hence, Length of latus rectum = 4a = 8<\/p>\n

(ii) The given parabola is of the form \\(x^2\\) = -4ay, where 4a = 16 i.e. a = 4.<\/p>\n

Hence, Length of latus rectum = 4a = 16<\/p>\n

Example<\/span><\/strong> : Find the latus rectum of the parabola \\(y^2 – 8y – x + 19\\) = 0<\/p>\n

Solution<\/strong><\/span> : The given equation is<\/p>\n

\\(y^2 – 8y – x + 19\\) = 0  \\(\\implies\\)  \\(y^2 – 8y\\) = x – 19<\/p>\n

\\(\\implies\\)  \\(y^2 – 8y + 16\\) = x – 19 + 16<\/p>\n

\\(\\implies\\)  \\((y – 4)^2\\) = (x – 3)<\/p>\n

The equation is of the form \\(y^2\\) = 4ax, where 4a = 1 i.e. a = 1\/4.<\/p>\n

Hence, Length of Latus Rectum is 4a = 1.<\/p>\n","protected":false},"excerpt":{"rendered":"

Here you will learn formula to find the length of latus rectum of parabola with examples. Let’s begin – Latus Rectum of Parabola A double ordinate through the focus is called the latus rectum i.e. the latus rectum of a parabola is a chord passing through the focus perpendicular to the axis. In the given …<\/p>\n

Length of Latus Rectum of Parabola Formula<\/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":[12],"tags":[],"yoast_head":"\nLength of Latus Rectum of Parabola Formula - Mathemerize<\/title>\n<meta name=\"description\" content=\"In this post you will learn formula to find the length of latus rectum of parabola with examples.\" \/>\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\/length-of-latus-rectum-of-parabola-formula\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Length of Latus Rectum of Parabola Formula - 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