{"id":3442,"date":"2021-07-24T13:14:49","date_gmt":"2021-07-24T13:14:49","guid":{"rendered":"https:\/\/mathemerize.com\/?p=3442"},"modified":"2021-11-20T22:09:57","modified_gmt":"2021-11-20T16:39:57","slug":"diameter-form-of-circle","status":"publish","type":"post","link":"https:\/\/mathemerize.com\/diameter-form-of-circle\/","title":{"rendered":"Diameter Form of Circle – Equation and Examples"},"content":{"rendered":"

Diameter Form of Circle Equation<\/h2>\n

The equation of the circle drawn on the straight line joining two points \\((x_1, y_1)\\) and \\((x_2, y_2)\\) is<\/p>\n

\n

(\\(x-x_1\\))(\\(x-x_2\\)) + (\\(y-y_1\\))(\\(y-y_2\\)) = 0<\/strong>.<\/p>\n<\/blockquote>\n

This is known as diameter form of circle<\/strong>.<\/p>\n

where \\((x_1, y_1)\\) and \\((x_2, y_2)\\)<\/strong> are coordinates of two ends of diameter of circle.<\/p>\n

Note<\/strong> – If the coordinates of the end points of a diameter of a circle are given, we can also find the equation of the circle by finding the coordinates of the center and radius. The center is the mid-point of the diameter and radius is half of the length of the diameter.<\/p>\n

Examples :<\/h2>\n\n\n

Example : <\/span> Find the diameter form of the circle, the coordinates of the end points of whose diameter are (-1, 2) and (4, -3). <\/p>\n

Solution : <\/span>Given coordinates of two ends of diameter of circle i.e. (-1, 2) and (4, -3).

\nWe know that the equation of the circle described on the line segment joining \\((x_1, y_1)\\) and \\((x_2, y_2)\\) as a diameter is

\n(\\(x-x_1\\))(\\(x-x_2\\)) + (\\(y-y_1\\))(\\(y-y_2\\)) = 0

\nHere, \\(x_1\\) = -1, \\(x_2\\) = 4, \\(y_1\\) = 2 and \\(y_2\\) = -3

\nSo, the equation of the required circle is

\n(x + 1)(x – 4) + (y – 2)(y + 3) = 0

\n\\(x^2 + y^2 – 3x + y – 10\\) = 0

<\/p>\n\n\n\n

Example : <\/span> Find the diameter form of the circle, drawn on the intercept made by the line 2x + 3y = 6 between the coordinates axes as diameter. <\/p>\n

Solution : <\/span>The line 2x + 3y = 6 meets X and Y axes at A(3, 0) and B(0, 2) respectively

\nWe know that the equation of the circle described on the line segment joining \\((x_1, y_1)\\) and \\((x_2, y_2)\\) as a diameter is

\n(\\(x-x_1\\))(\\(x-x_2\\)) + (\\(y-y_1\\))(\\(y-y_2\\)) = 0

\nTaking AB as a diameter, the equation of the required circle is

\n(x – 3)(x – 0) + (y – 0)(y – 2) = 0

\n\\(x^2 + y^2 – 3x – 2y\\) = 0

<\/p>\n\n\n\n

\n
Next – Equation of Tangent to a Circle <\/a><\/div>\n<\/div>\n\n\n\n
\n
Previous – General Equation of the Circle | Standard Form of Circle<\/a><\/div>\n<\/div>\n","protected":false},"excerpt":{"rendered":"

Diameter Form of Circle Equation The equation of the circle drawn on the straight line joining two points \\((x_1, y_1)\\) and \\((x_2, y_2)\\) is (\\(x-x_1\\))(\\(x-x_2\\)) + (\\(y-y_1\\))(\\(y-y_2\\)) = 0. This is known as diameter form of circle. where \\((x_1, y_1)\\) and \\((x_2, y_2)\\) are coordinates of two ends of diameter of circle. Note – If …<\/p>\n

Diameter Form of Circle – Equation and 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":[23],"tags":[181,185,186],"yoast_head":"\nDiameter Form of Circle - Equation and Examples<\/title>\n<meta name=\"description\" content=\"In this post, you will learn what is diameter form of circle equation and how to find equation of circle in diameter form with example.\" \/>\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\/diameter-form-of-circle\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Diameter Form of Circle - 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