in part a you would work out what y^2 is and what x^2 is from the information you have - as the answer is in terms of them. Then to combine those two equations together you need to play around with some identities. I change y^2 = 9sin^2(2t) into 9(1-cos^2(2t)) then worked out what cos(2t) was in terms of x as cos(2t) = 1 - 2sin^2(t).
for part b, you plug in the y^2 formula into the equation of a circle x^2 + y^ = r^2 (as they intersect, we can do simultaneous equations). Once you’ve got an expression for that, c1 intersects c2 such that the radius is as big as possible - hence it only touches 4 times. This means we should make dr/dx = 0 and solve it to get a maximum r value.