hi im new to this but i found a really hard problem that I've been stuck on for hours.

The circles C_{1 }and C_{2} are defined by the equations x^{2} +y^{2} =1 and (x-2)^{2} +y^{2} = 16 respectively. Find the locus of the centers (a, b) of all circles externally tangent to C_{1} and internally tangent to C2 Enter your answer in the form P(a^{2}) + Q(b^{2}) + R(a) + S(b) + T = 0 where all the coeficcents are integers, P is positive and GCD(P, Q, R, S, T) = 1.

I have a sneaky suspicion that the locus is a circle but its difficult to prove as it could be an ellipse or something of that sort. If anyone could help that would be soo appreciated!

Guest Apr 12, 2023