# Given the equation of a circle: (x-3)^2+(y+2)^2=25, how do you find the center and the radius?

Dec 9, 2015

center: $\left(3 , - 2\right)$
radius: $5$

#### Explanation:

The general form for the equation of a circle with center $\left(\textcolor{red}{a} , \textcolor{b l u e}{b}\right)$ and radius $\textcolor{g r e e n}{r}$ is
$\textcolor{w h i t e}{\text{XXX}} {\left(x - \textcolor{red}{a}\right)}^{2} + {\left(y - \textcolor{b l u e}{b}\right)}^{2} = {\textcolor{g r e e n}{r}}^{2}$

${\left(x - 3\right)}^{2} + {\left(y + 2\right)}^{2} = 25$
can be easily transformed into the general form as:
$\textcolor{w h i t e}{\text{XXX}} {\left(x - \textcolor{red}{3}\right)}^{2} + {\left(y - \textcolor{b l u e}{\left(- 2\right)}\right)}^{2} = {\textcolor{g r e e n}{5}}^{2}$