{"id":1207,"date":"2012-03-15T17:27:26","date_gmt":"2012-03-15T17:27:26","guid":{"rendered":"http:\/\/www.SchoolTutoring.com\/help\/?p=1207"},"modified":"2014-12-02T08:33:47","modified_gmt":"2014-12-02T08:33:47","slug":"equations-of-a-circle","status":"publish","type":"post","link":"https:\/\/schooltutoring.com\/help\/equations-of-a-circle\/","title":{"rendered":"Equations of a Circle"},"content":{"rendered":"

A circle is the set of all points that are the same distance, r, from a fixed point called center.
\n\"\"<\/a><\/p>\n

 <\/p>\n

If (x, y) is any point on the circle whose center is at (a, b) then the radius r of the circle is:<\/p>\n

According to Pythagorean Theorem (Square of hypotenuse is sum of square of other two sides of the right triangle):<\/p>\n

(x – a)2<\/sup> + (y – b)2<\/sup> = r2<\/sup>\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 <\/strong><\/p>\n

The above equation is called the Standard Form<\/strong> of equation of a circle. This form is also referred as center-radius form of equation of a circle.<\/p>\n

The above equation can be simplified to get the General Form<\/strong> of equation of a circle.<\/p>\n

(x2<\/sup> \u2013 2ax + a2<\/sup>) + (y2<\/sup> \u2013 2by + b2<\/sup>) = r2<\/sup><\/p>\n

x2 <\/sup>+ y2<\/sup> \u2013 2ax \u2013 2by + a2<\/sup> + b2<\/sup> = r2<\/sup><\/strong><\/p>\n

which can also be written as:<\/p>\n

x2 <\/sup>+ y2 <\/sup>+ Ax + by + C = 0<\/strong><\/p>\n

where, A = -2a, B = -2b and C = a2<\/sup> + b2 <\/sup>\u2013 r2<\/sup><\/p>\n

General form of equation of circle can be converted to standard form by using completing the square method.<\/p>\n

Example 1:<\/p>\n

What is the equation of the circle with radius 5 and center at (-2, 3)?<\/p>\n

Here, a = -2, b = 3 and r = 5<\/p>\n

Using standard form of equation:<\/p>\n

(x \u2013 (-2))2<\/sup> + (y \u2013 3)2<\/sup> = 52<\/sup><\/p>\n

(x + 2)2<\/sup> + (y \u2013 3)2<\/sup> = 25<\/p>\n

This can also be written in general form as<\/p>\n

x2<\/sup> + y2<\/sup> \u2013 2(-2)x \u2013 2(3)y + (-2)2<\/sup> + 32<\/sup> = 52<\/sup><\/p>\n

x2<\/sup> + y2<\/sup> + 4x \u2013 6y + 4 + 9 = 25<\/p>\n

x2<\/sup> + y2<\/sup> + 4x \u2013 6y + 13 = 25<\/p>\n

x2<\/sup> + y2<\/sup> + 4x \u2013 6y \u2013 12 = 0<\/p>\n

Example 2:<\/p>\n

Convert x2<\/sup> + y2<\/sup> \u2013 4x \u2013 2y \u2013 6 = 0 to standard form.<\/p>\n

(x2<\/sup> \u2013 4x) + (y2<\/sup> \u2013 2y) = 6<\/p>\n

(x2<\/sup> \u2013 4x +\u00a0 4) + (y2<\/sup> \u2013 2y + 1) = 6 + 4 + 1<\/p>\n

(x\u00a0 – 2)2<\/sup> + (y \u2013 1)2<\/sup> = 11<\/p>\n

(2, 1) is the center of the circle whose radius is \u221a11.<\/p>\n

 <\/p>\n

SchoolTutoring Academy is the premier educational services company for K-12 and college students. We offer tutoring programs for students in K-12, AP classes, and college. To learn more about how we help parents and students in Toronto visit: Tutoring in Toronto<\/a>.<\/p>\n

 <\/p>\n","protected":false},"excerpt":{"rendered":"

A circle is the set of all points that are the same distance, r, from a fixed point called center.   If (x, y) is any point on the circle whose center is at (a, b) then the radius r of the circle is: According to Pythagorean Theorem (Square of hypotenuse is sum of square […]<\/p>\n","protected":false},"author":19,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"_acf_changed":false,"inline_featured_image":false,"footnotes":""},"categories":[10],"tags":[251,592,723,1724],"class_list":["post-1207","post","type-post","status-publish","format-standard","hentry","category-geometry","tag-centerradiusformofcircle","tag-equationsofceircle","tag-generalformofequationofcircle","tag-standardformofequationofcircle"],"acf":[],"aioseo_notices":[],"_links":{"self":[{"href":"https:\/\/schooltutoring.com\/help\/wp-json\/wp\/v2\/posts\/1207","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/schooltutoring.com\/help\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/schooltutoring.com\/help\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/schooltutoring.com\/help\/wp-json\/wp\/v2\/users\/19"}],"replies":[{"embeddable":true,"href":"https:\/\/schooltutoring.com\/help\/wp-json\/wp\/v2\/comments?post=1207"}],"version-history":[{"count":0,"href":"https:\/\/schooltutoring.com\/help\/wp-json\/wp\/v2\/posts\/1207\/revisions"}],"wp:attachment":[{"href":"https:\/\/schooltutoring.com\/help\/wp-json\/wp\/v2\/media?parent=1207"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/schooltutoring.com\/help\/wp-json\/wp\/v2\/categories?post=1207"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/schooltutoring.com\/help\/wp-json\/wp\/v2\/tags?post=1207"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}