# How do you find the center-radius form of the equation of the circle given Center (0,-2), radius 6?

May 23, 2016

${\left(x - 0\right)}^{2} + {\left(y - \left(- 2\right)\right)}^{2} = {6}^{2}$

#### Explanation:

The center-radius form of the equation of a circle is:

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

where $\left(h , k\right)$ is the center and $r$ the radius.

So in our example, we can write:

${\left(x - 0\right)}^{2} + {\left(y - \left(- 2\right)\right)}^{2} = {6}^{2}$

If we are slightly less fussy about the form, this simplifies to:

${x}^{2} + {\left(y + 2\right)}^{2} = 36$