diff --git a/guide/english/mathematics/circle-equations/index.md b/guide/english/mathematics/circle-equations/index.md index 639607034e..afc8b0c7fb 100644 --- a/guide/english/mathematics/circle-equations/index.md +++ b/guide/english/mathematics/circle-equations/index.md @@ -35,7 +35,19 @@ for, ![0<=t<= 2 pi](https://raw.githubusercontent.com/pranabendra/articles/master/geometry/circle/circle_5.png) +### 3. Diametric form: +Suppose there are two points on a circle (x1, y1) and (x2, y2), such that they lie on the opposite ends of the same diameter. Then the equation of circle can be written as: +``` +(x-x1)(x-x2) + (y-y1)(y-y2) = 0 +``` +Suppose 2 points on the circle A = (x1, y1) and B = (x2, y2) are diametrically opposite, then for any point C = (x,y) on the circle, ΔABC will be a right triangle with right angle at C. This implies + +``` +AC ⊥ BC +(mAC)*(mBC) = -1 +``` + +Substituting the values for slopes, we get: (x-x1)(x-x2) + (y-y1)(y-y2) = 0 + ### More Information: Equation of a Circle - -