# Another Ellipse Problem

Geometry Level 4

A variable point $$P$$ on an ellipse of eccentricity $$e=\dfrac{1}{8}$$, is joined to it's focii $$S_1$$ and $$S_2$$.

Given that the locus of the incentre of the triangle $$\Delta P S_1 S_2$$ comes out to be a conic;

Evaluate its eccentricity $$e'$$. Now $$e'$$ is of the form $$\frac{\sqrt{a}}{b}$$, where $$a$$ and $$b$$ are coprime positive integers, find $$a\times b$$.

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