I have some trouble with this exercise. It says as follows: Find the constrained extremes for over

I think that difficult of this problem is that I have a family of circles that satisfies , the family of circles with radius .

This is what I did.

From (1) and (2): (*)

Replacing with (*) in (1)

Replacing in (3)

Well, I'm not sure if this is okey. If it is, how should I proceed?

Thanks for posting!