If a variable circle S touches S1 : |z - z1| = r1 internally and S2 : |z - z2| = r2 externally while

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If a variable circle S touches S1 : |z - z1| = r1 internally and S2 : |z - z2| = r2 externally while the curves S1 & S2 touch internally to each other. Then the eccentricity of the locus of the centre of the curve S is equal to

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c1c2 = r1 - r2|z1 - z2| = r1 - r2 ..... (1)cc1 = r1 - r ..... (2) |z - z1| = r1 - r cc2 = r + r2|z - z2| = r + r2 ..... (3)(2 ) + (3) |z - z1| + |z - z2| = r1 + r22a = r1 + r2 |z1 - z2| = 2ae = r1 - r2e =

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