Find the equation of the circle with center at (-2, -3) and passing through the point (2,5).

1. Identify the center of the circle (h, k) = (-2, -3) .
2. Use the distance formula to find the radius r :
r = \sqrt{(x_1 - x_2)^2 + (y_1 - y_2)^2}
where (x_1, y_1) = (2, 5) and (x_2, y_2) = (-2, -3) .
3. Calculate the radius:
r = \sqrt{(2 - (-2))^2 + (5 - (-3))^2}
r = \sqrt{(2 + 2)^2 + (5 + 3)^2}
r = \sqrt{4^2 + 8^2}
r = \sqrt{16 + 64}
r = \sqrt{80}
r = 4\sqrt{5}
4. Write the equation of the circle using the standard form:
(x - h)^2 + (y - k)^2 = r^2
where h = -2 , k = -3 , and r = 4\sqrt{5} :
(x + 2)^2 + (y + 3)^2 = (4\sqrt{5})^2
(x + 2)^2 + (y + 3)^2 = 80

[Answer] (x + 2)^2 + (y + 3)^2 = 80