Answer
$\left( x+7 \right)^2+\left( y+9 \right)^2=11$
Work Step by Step
Using the standard form of the equation of circles which is given by $(x-h)^2+(y-k)^2=r^2$ where the center is $(h,k)$ and radius $r$, then the equation of the circle with the given center at $
(-7,-9)
$ and the given radius is $
\sqrt{11}
$ is
\begin{array}{l}
\left( x-(-7) \right)^2+\left( y-(-9) \right)^2=(\sqrt{11})^2\\\\
\left( x+7 \right)^2+\left( y+9 \right)^2=11
.\end{array}
