and are the ends of the diameter of a circle. Show that the equation of the circle is:

.

If A and B are also points on the hyperbola and the circle on AB as diameter cuts the hyperbola again at C and D, prove that CD is a diameter of the hyperbola.

I can't prove the first part. I got:

, instead of the given equation. I found this from the midpoint of AB and half the length of AB.

Thanks!