Hello arzeBy completing the square, re-write as to note that this circle has centre and radius . The circle has centre and radius . So the circles are positioned as in the attached diagram.

Using similar triangles, can you see that ?

The coordinates of are therefore fairly obvious.

The centre of the circle through lies on the perpendicular bisector of - and also, by symmetry, on the -axis. Can you work out the coordinates of this centre, and the radius of the circle now? Its equation is then very straightforward to write down.

Get back to us if you still need more help.

Grandad