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9. Let C 1 and C 2 be two circles with C 2 lying inside C 1 . A circle C lying inside C 1 touches C 1 internally and C 2 externally. Identify the locus of the centre of C. appeared in 2001. Please post a good solution

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

Grade:12

1 Answers

ruchi yadav
askIITians Faculty 27 Points
7 years ago
Let equation of circle C1 is x2+y2 = r2 , with center A1(0.0)
and equation of C2 is (x-a)2 + (y-b)2 = d2, with center A2 (a,b)


let A (h,k) is the center of circle C and radius is p,

A1A = r-p

A2A = d+p

adding both the equations ,

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)









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