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Q.

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
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