Question

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

Answer 1

Let the given circles C₁ and C₂ have centres O₁ and O₂ and radii r₁ and r₂ respectively.

Let the variable circle C touching C₁ internally, C₂ externally have a radius r and centre at O.

Alternate Solution

which represents an ellipse whose foci are at (a,b) and (0,0).