Answer
The center of the circle is (1,-2), and its radius is about 5.66 units.
The equation is $(x-1)^2+(y+2)^2=32$
Work Step by Step
In order to find the center using these points, we find the midpoint between them:
$h=\dfrac{5+(-3)}{2},k=\dfrac{-6+2}{2}$
$h=\dfrac{2}{2},k=\dfrac{-4}{2}$
$h=1, k=-2$
Now, we can use the center and one of the points to find the distance between them, which is the radius:
$r=\sqrt{(1-5)^2+(-2-(-6))^2}$
$r=\sqrt{(-4)^2+(4)^2}$
$r=\sqrt{16+16}$
$r=\sqrt{32}\approx5.66$ units
The equation would then be:
$(x-1)^2+(y-(-2))^2=(\sqrt{32})^2$
$(x-1)^2+(y+2)^2=32$