# How do you write the equation for a circle with center (–7 –6) and radius 2?

Jun 6, 2016

${\left(x + 7\right)}^{2} + {\left(y + 6\right)}^{2} = 4$

#### Explanation:

The general form for the equation of a circle is
$\textcolor{w h i t e}{\text{XXX}} {\left(x - \textcolor{red}{a}\right)}^{2} + {\left(y - \textcolor{b l u e}{b}\right)}^{2} = {\textcolor{g r e e n}{r}}^{2}$
where the circle's center is at $\left(\textcolor{red}{a} , \textcolor{b l u e}{b}\right)$
and the circle's radius is $\textcolor{g r e e n}{r}$

Substituting $\left(\textcolor{red}{- 7} , \textcolor{b l u e}{- 6}\right)$ for $\left(\textcolor{red}{a} , \textcolor{b l u e}{b}\right)$
and color(green)(2)$f \mathmr{and}$color(green)(r)#

$\textcolor{w h i t e}{\text{XXX}} {\left(x - \left(\textcolor{red}{- 7}\right)\right)}^{2} + {\left(y - \left(\textcolor{b l u e}{- 6}\right)\right)}^{2} = {\textcolor{g r e e n}{r}}^{2}$

which can be simplified as:
$\textcolor{w h i t e}{\text{XXX}} {\left(x + 7\right)}^{2} + {\left(y + 6\right)}^{2} = 4$