# What is the general form of the equation of a circle with a center at the origin and a radius of 9?

Mar 4, 2016

${x}^{2} + {y}^{2} = 81$

#### Explanation:

A circle of radius $r$ centered at a point $\left({x}_{0} , {y}_{0}\right)$ has the equation

${\left(x - {x}_{0}\right)}^{2} + {\left(y - {y}_{0}\right)}^{2} = {r}^{2}$

Substituting $r = 9$ and the origin $\left(0 , 0\right)$ for $\left({x}_{0} , {y}_{0}\right)$ this gives us

${x}^{2} + {y}^{2} = 81$