Answer
$(x+4)^2+(y-3)^2=4$
Work Step by Step
$\bf{\text{Solution Outline:}}$
Use the Center-Radius Form of the equation of circles to get the equation with the given center, $C(
-4,3
),$ and the given radius, $r=
2
.$
$\bf{\text{Solution Details:}}$
With the given center, then $h=
-4
$ and $k=
3
.$ Using the Center-Radius Form of the equation of circles which is given by $(x-h)^2+(y-k)^2=r^2, $ the equation of the circle is
\begin{array}{l}\require{cancel}
(x-(-4))^2+(y-3)^2=(2)^2
\\\\
(x+4)^2+(y-3)^2=4
.\end{array}
