Answer
$\left( x+4 \right)^2+\left( y-4 \right)^2=9$
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 $
(-4,4)
$ and the given radius is $
3
$ is
\begin{array}{l}
\left( x-(-4) \right)^2+\left( y-4 \right)^2=3^2\\\\
\left( x+4 \right)^2+\left( y-4 \right)^2=9
.\end{array}
