endpoints of the diameter are (4,-10) and (-4,5)
the midpoint of the endpoints of a diameter is the center.
To find the midpoint, average the x's and average the y's, so (0, -2.5). This is the center.
The equation of the circle centered at (x0,y0) with radius r is
( x - x0 )2 + ( y - y0 )2 = r2 (1)
Plugging in the center we get
( x - 0 )2 + ( y - (-2.5) )2 = r2 or x2 + ( y + 2.5 )2 = r2 (2)
Using either endpoint of the diameter as a point on the circle we can get r2.
42 + ( -10 + 2.5 )2 = r2 or r2 = 16 + (-7.5)2 = 72.25
Plugging this back into (2) we get
x2 + ( y + 2.5 )2 = 72.25
