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If a variable circle S touches S1 : |z-...

If a variable circle S touches `S_1 : |z-z_1|=7` internally and `S_2:|z-z_2|=4` externally while the curve `S_1 and S_2` touch internally to each other, `(z_1!=z_2|`. If the eccentricity of the locus of the centre of the curve S in e find the value of 11e.

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