If \( P \) is a variable point on the ellipse \( \frac{x^{2}}{a^{2}...

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If \( P \) is a variable point on the ellipse \( \frac{x^{2}}{a^{2}}+\frac{y^{2}}{b^{2}}=1 \) whose focii are \( S \) and \( S^{\prime} \) and \( e_{1} \) is the eccentricity and
\( \mathrm{P} \) the locus of the incentre of \( \triangle \mathrm{PSS}^{\prime} \) is an ellipse whose eccentricity is \( \mathrm{e}_{2} \), then the value of \( \left(1+\frac{1}{\mathrm{e}_{1}}\right) \mathrm{e}_{2}^{2} \) is

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