Answer
$(x+12)^2+(y-13)^2=7$
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, $C(
-12,13
),$ and the given radius, $r=
\sqrt{7}
.$
$\bf{\text{Solution Details:}}$
With the given center, then $h=
-12
$ and $k=
13
.$ 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-(-12))^2+(y-13)^2=(\sqrt{7})^2
\\\\
(x+12)^2+(y-13)^2=7
.\end{array}
