# Equation of a Circle Formula

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**

\[\LARGE (x – a)^{2} + (y – b)^{2} = r^{2}\]

Where,

a, b is the center,

r is the radius

**General form of Circle Equation**

$\LARGE x^{2} + y^{2} + Ax + By + C = 0$

#### 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,

$(x-a)^{2}$ + $(y-b)^{2}$ = $r^{2}$

So, $(x-4)^{2}$ + $(y-5)^{2}$ = $7^{2}$

So, $(x-4)^{2}$ + $(y-5)^{2}$ = 49