a complex analysis question

From: wannabe mathematician (crooner_kwon_at_hotmail.com)
Date: 07/11/04 

Date: 11 Jul 2004 11:56:39 -0700

f(z)=(z_0 - z) / (1 - bar{z_0} z) abs(z_0)<1 conformal mapping.(unit
disk to unit disk)

Suppose f maps a disk (center s, radius s) on to a disk (center 0
radisu r)
where s>0, 2s<1, r<1

(1) For s=1/4, determine f(z) and r.
(2) Show that, in general, r and s are related by the equation

r^2s-r+s=0

---------------(sorry for clumsy notation)-----------

I think, there might be some symmetric relation between those two
disks in a unit disk. But I cannot figure that out. How can I solve
this problem?

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