The general equation for a circle centered at (x0, y0) with radius r is given by
( x - x0 )2 + ( y - y0 )2 = r2 (1)
and we are given the center is at (-2,8). So plugging these into (1) we get
( x - (-2) )2 + ( y - 8 )2 = r2 or ( x + 2 )2 + ( y - 8 )2 = r2 (2)
We are also given a point on the circle, (1,4). Plugging this into (2) lets us find r2.
( 1 + 2 )2 + ( 4 - 8 )2 = r2 giving r2 = 32 + (-4)2 = 9 + 16 = 25.
Substituting this back into (2) gives
( x + 2 )2 + ( y - 8 )2 = 25
