Let circles C1 and C2 on Argand plane be given by z+1=3 and z-2=7 respectively. If a variable circle C be such that it touches C1 externally and C2 internally .The locus of center of variable circle describes a conic E. If eccentricity of E can be written in simplest from and p/q when p, q then find the value of |q – p|
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answer is 2.
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Detailed Solution
(h+1)2+k2=3+r and (h-2)2+k2=7-rRequired locus is ellipse(x+1)2+y2+(x-2)2+y2=10having focii are (-1,0) and (2,0)2ae=3 , e=310