9. Let C1 and C2 be two circles with C2 lying inside C1. A circle C lying inside C1touches C1 internally and C2 externally. Identify the locus of the centre of C.

appeared in 2001. Please post a good solution

under root of (h2+k2) +under root of ((h-a)2+(k-b)2) = r+ d

For locus , replace h by x and k by y

so resulting equation is ellipse with foci at A1 (0,0) and A2 (a,b) and lenght of major axis as r + d.

Thanks,

Ruchi ( Askiitian's faculty)