Answer
$(x+1)^2+(y-2)^2=5^2$.
Work Step by Step
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: $r=\sqrt{(3-(-1))^2+(5-2)^2}=\sqrt{16+9}=\sqrt{25}=5.$
$C=(-1,2)$, hence our equation: $(x-(-1))^2+(y-2)^2=5^2\\(x+1)^2+(y-2)^2=5^2$.
