The ends of the diameter are (-16, -8) and (12,4)
The point midway between those points is
x = (1/2) (-16+12) = (1/2) (-4) = -2
y = (1/2) (-8+4) = (1/2) ( -4) = -2
So the point (-2, -2) is the center of the circle.
The ends of the diameter are (-16, -8) and (12,4)
The distance between those points is . . .
the square root of (12+16)² + (4+8)² =
square root of (28)² + (12)² =
square root of (784 + 144) =
square root of (928)
The diameter of the circle is √928 ,
so its radius is (1/2)√928 = √232 .
Now that we know the center and the radius,
we can write the equation of the circle:
(x + 2)² + (y + 2)² = 232