Answer
$(x-1)^2+(y+2)^2=(4\sqrt2)^2$.
Work Step by Step
$C$ is the midpoint of the two given points, hence $C=(\frac{-3+5}{2},\frac{2-6}{2})=(1,-2).$
The general equation for a circle with radius $r$ and centre $(h,k)$ is: $(x-h)^2+(y-k)^2=r^2$.
The distance formula from $P_1(x_1,y_1)$ to $P_2(x_2,y_2)$ is $d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$.
Hence here: $r=\sqrt{(-3-1)^2+(2-(-2))^2}=\sqrt{16+16}=\sqrt{32}=4\sqrt2.$
Hence our equation: $(x-1)^2+(y+2)^2=(4\sqrt2)^2$.
