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Let C(1) and C(2) be two circles with C...

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.

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Ellipse having foci are ( a,b) and ( 0,0)
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