Answer
$(x+1)^2+(y-4)^2 = 52$
Work Step by Step
We can write the general equation for a circle:
$(x-a)^2+(y-b)^2 = r^2$
where $(a,b)$ is the center of the circle and $r$ is the radius
The center of this circle is $(-1,4)$
We can find the radius:
$r = \sqrt{(-1-3)^2+(4-(-2))^2}$
$r = \sqrt{(-4)^2+(6)^2}$
$r = \sqrt{16+36}$
$r = \sqrt{52}$
We can write the equation of this circle:
$(x-a)^2+(y-b)^2 = r^2$
$(x+1)^2+(y-4)^2 = 52$
