# How do you find the equation for a circle with center is (-2,-3) and radius 3?

Dec 2, 2015

The equation for a circle with centre $\left(h , k\right)$ and radius $r$ can be written in standard form as:

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

In our case:

${\left(x + 2\right)}^{2} + {\left(y + 3\right)}^{2} = 9$

#### Explanation:

A standard form for the equation of a circle of radius $r$ and centre $\left(h , k\right)$ is:

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

In our case $h = - 2$, $k = - 3$ and $r = 3$, so:

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

or more simply:

${\left(x + 2\right)}^{2} + {\left(y + 3\right)}^{2} = 9$