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A circle S=0 touches a circle S(1)=x^(2)...

A circle S=0 touches a circle `S_(1)=x^(2)+y^(2)-4x+6y-23=0` internally and the circle `S_(2)=x^(2)+y^(2)-4x+8y+19=0` externally. The locus of centre S=0 is a conic whose eccentricity is e and `r_(1) and r_(2)` be the radius of `S_(1)` & `S_(2) ` respectively and `[*]` denotes greatest integer, then

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