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Circle equation problem

• To: mathgroup at smc.vnet.net
• Subject: [mg61525] Circle equation problem
• From: Daniele Lupo <danwolf80_no_spam_ at libero.it>
• Date: Fri, 21 Oct 2005 00:38:10 -0400 (EDT)
• Sender: owner-wri-mathgroup at wolfram.com

Hi to all.

I've this equation:

Abs[p]^2 == Abs[(G - X + I*Y)/(-1 + G*(X + I*Y))]^2

It represent a circle in the complex plane; X and Y are coordinates in the
complex plane (point is X + I Y), while G, p are complex parameters.

I want to write it in this standard form for a circle in the cartesian
plane:

(X - Xcenter)^2 + (Y - YCenter)^2 - ray^2 == 0

In this way, the center in the complex plane is XCenter + I YCenter, 

With some effort I think to be able to solve it by hand, but I want to know
if there's a (easy?) way to find center and ray of the circle with
Mathematica. How can I find Xcenter, YCenter and ray from the original
equation?

Thanks for your answers.

Daniele Lupo

PS: Thank you for all your replies in my previous posts!!! :-)