# How do you find the equation of the circle with center (–7, –6) and radius 2?

Jan 22, 2016

${\left(x + 7\right)}^{2} + {\left(y + 6\right)}^{2} = 4$

#### Explanation:

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

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

From the information provided, we know that $h = - 7 , k = - 6 ,$ and $r = 2$, hence the equation

${\left(x - \left(- 7\right)\right)}^{2} + {\left(y - \left(- 6\right)\right)}^{2} = {2}^{2}$

Which yields, when simplified

${\left(x + 7\right)}^{2} + {\left(y + 6\right)}^{2} = 4$

Graphed:

graph{((x+7)^2+(y+6)^2-4)((x+7)^2+(y+6)^2-.02)=0 [-17, 5, -10, 1]}