If F1 and F2 be the feet of the perpendicular from the foci S1 and S2 of an ellipse x25+y23=1on the tangent at any point P on the ellipse, then S1F1S2F2 is equal to

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If $F_{1}$ and $F_{2}$ be the feet of the perpendicular from the foci $S_{1}$ and $S_{2}$ of an ellipse $\frac{x^{2}}{5} + \frac{y^{2}}{3} = 1$ on the tangent at any point P on the ellipse, then $(S_{1} F_{1}) (S_{2} F_{2})$ is equal to

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answer is 3.

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Detailed Solution

We know that the product of perpendiculars from two foci of an ellipse upon any tangent is equal to the square of the semi-minor axis.

$\begin{array}{ll} ∴ (S_{1} F_{1}) (S_{2} F_{2}) = 3 \end{array}$

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