Equation of a Circle Formula

Circle equation formula refers to the equation of a circle which represents the center-radius form of the circle. To recall, circle is referred to a round shape boundary where all the points are equidistant from the centre. An equation is generally required to represent the circle. There are basically two forms of representation:

  1. Standard Form
  2. General Form

Standard Form of Circle Equation

(x – a)2 + (y – b)2 = r2

Where,

  • a, b is the center, 
  • r is the radius

General form of Circle Equation

x2 + y2 + Ax + By + C = 0

Solved Examples

Question 1: If the center point and radius of a circle is given as (4, 5) and 7 respectively. Represent this as a circle equation ?

Solution:

Given parameters are

Center (a, b) = (4, 5);

radius r = 7

The standard form of circle equation is,

(x − a)2 + (y − b)2 = r2

So, (x − 4)2 + (y − 5)2 = 72

So, (x − 4)2 + (y − 5)2 = 49

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