Question

Write the equation in standard form of the circle which passes through (-2, 16) and has x-intercepts -2 and -32.

Answer 1

If it passes through (-2,16) and (-2,0) and (-32,0) then by symmetry the center must be at (-17,8)

Now we can use any of the points to find that r = 17 so

(x+17)^2 + (y-8)^2 = 17^2

see

http://www.wolframalpha.com/input/?i=plot+%28x%2B17%29^2+%2B+%28y-8%29^2+%3D+17^2,+x%3D-2,y%3D16,x%3D-32,y%3D0