You don't need calculus for this -- just a good sense of fundamental coordinate geometry -- but this is
not a GMAT question. This strikes me as the sort of question you'd see in a honors Precalculus or Algebra II class, and the idea is to ask you to provide a proof that requires you to "think in letters" and thus divine general algebraic relationships.
I took a crack at it and I *think* I have the right answer. I figured the solution would be unreadable in ASCII, and Beat the GMAT doesn't seem to allow LaTeX on the boards, so I attached the steps as a file. I didn't explain any of my steps, but the only step that seems to require beyond-the-GMAT algebra is the second one, where you complete the square to find the equation of the circle and then use that equation to get the center of the circle.
Any lazy calculus students who are Googling for a proof of this sometime in 2016 or so are required to click Thanks if they use it for a homework assignment.
