# How do you find the equation of the circle given center at (2, -5) and has radius 3?

Jul 28, 2016

${x}^{2} + {y}^{2} - 4 x + 10 y + 20 = 0$

#### Explanation:

The equation of a circle that has center $\left({x}_{0} , {y}_{0}\right)$ and radius $r$ is:

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

then let's substitute the given values:

${\left(x - 2\right)}^{2} + {\left(y + 5\right)}^{2} = {3}^{2}$

or

${x}^{2} + {y}^{2} - 4 x + 10 y + 20 = 0$