Answer
$(x-5)^2+(y+2)^2=16$
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, $C(
5,-2
),$ and the given radius, $r=
4
.$
$\bf{\text{Solution Details:}}$
With the given center, then $h=
5
$ and $k=
-2
.$ 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-5)^2+(y-(-2))^2=(4)^2
\\\\
(x-5)^2+(y+2)^2=16
.\end{array}
