# How do you write the equation of the circle with center at (5,-3) and radius of 4?

Jan 22, 2016

${\left(x - 5\right)}^{2} + {\left(y + 3\right)}^{2} = 16$

#### 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 $h = 5 , k = - 3 ,$ and $r = 4$, hence the equation

${\left(x - 5\right)}^{2} + {\left(y - \left(- 3\right)\right)}^{2} = {4}^{2}$

Which yields, when simplified

${\left(x - 5\right)}^{2} + {\left(y + 3\right)}^{2} = 16$

Graphed:

graph{((x-5)^2+(y+3)^2-16)((x-5)^2+(y+3)^2-.02)=0 [-7.45, 15.07, -8.27, 2.98]}