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

The circles  Cand 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!

 Apr 12, 2023
 #3
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The answer is a^2 - 4a + 4b^2 - 12 = 0.

 Apr 12, 2023
 #4
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why, could you provide a proof or what kind of shape the locus is?

Guest Apr 12, 2023

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