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Let C1and C2 be two circles with C2 lyin...

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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`:.` Locus of O is an ellipse with foci `O_(1)andO_(2)`.
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