If F1 and F2 are the feet of perpendiculars from foci S1 and S2 of an ellipse x25+y23=1 on the tangent at any point P on the ellipse then (S1F1) (S2F2) =

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If F₁ and F₂ are the feet of perpendiculars from foci S₁ and S₂ of an ellipse $\frac{x^{2}}{5} + \frac{y^{2}}{3} = 1$ on the tangent at any point P on the ellipse then (S₁F₁) (S₂F₂) =

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answer is 3.

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Detailed Solution

Given Ellipse is

$\frac{x^{2}}{5} + \frac{y^{2}}{3} = 1 w h e r e a^{2} = 5, b^{2} = 3 (a > b) w e k n o w t h a t p r o d u c t o f p e r p e n d i c u l a r d i s \tan c e s f r o m f o c i t o a n y \tan g e n t i s b^{2} \Rightarrow (S_{1} F_{1}) (S_{2} F_{2}) = b^{2} = 3$