# What is the equation of the circle with a center at (3 ,1 ) and a radius of 2 ?

Jan 26, 2016

${\left(x - 3\right)}^{2} + {\left(y - 1\right)}^{2} = 4$

#### Explanation:

The standard form of a circle with a center at $\left(h , k\right)$ and a radius $r$ is

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

Since the center is $\left(3 , 1\right)$ and the radius is $2$, we know that

$\left\{\begin{matrix}h = 3 \\ k = 1 \\ r = 2\end{matrix}\right.$

Thus, the equation of the circle is

${\left(x - 3\right)}^{2} + {\left(y - 1\right)}^{2} = {2}^{2}$

This simplifies to be

${\left(x - 3\right)}^{2} + {\left(y - 1\right)}^{2} = 4$