hi im new to this but i found a really hard problem that I've been stuck on for hours.
The circles C1 and C2 are defined by the equations x2 +y2 =1 and (x-2)2 +y2 = 16 respectively. Find the locus of the centers (a, b) of all circles externally tangent to C1 and internally tangent to C2 Enter your answer in the form P(a2) + Q(b2) + 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!
