Find the distance of the two endpoints (-4, -9) and (8, -1).

d = √[(x_{1} - x_{2})^{2} + (y_{1} - y_{2})^{2}] = √[(-4 - 8)^{2} + (-9 - (-1))^{2}]

= √[(-12)^{2} + (-8)^{2}]√ = √(144 + 64) = √208 = √(16*13) = 4√13 ≈ 14.42 units

The radius of the circle, r, is 7.21 units, which is half of the diameter, d.

Find the center of the circle (midpoint of the diameter).

X_{midpoint}: [(-4 + 8)/2] = 4/2 = 2 Y_{midpoint}: [(-9 + (-1))/2] = -10/2 = -5

h = 2 and k = -5

The equation of the circle is (x - h)^{2} + (y - k)^{2} = r^{2}.

(x - 2)^{2} + (y - (-5))^{2} = (7.21)^{2} → **(x - 2)**^{2}** + (y + 5)**^{2}** = 52**