# How do you find the center and radius for x^2+(y-3)^2=16?

Apr 15, 2017

See below.

#### Explanation:

This is a circle, and the standard form is:

${\left(x - h\right)}^{2} + {\left(y - k\right)}^{2} = {r}^{2}$, where $\left(h , k\right)$ is the vertex, and $r$ is the radius.

The equation you want can be rewritten as:
${\left(x - 0\right)}^{2} + {\left(y - 3\right)}^{2} = {4}^{2}$

So, the center is $\left(0 , 3\right)$, and the radius is $4$.