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Let $P_{i}$ and $P_{i}'$ be the feet of the perpendiculars drawn from foci $S, S'$ on a tangent $T_{i}$ to an ellipse whose length of semi- major axis is 20, if $\sum_{t = 1}^{10} (S P_{i}) (S' P_{i}') = 2560$ then the value of eccentricity is

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Detailed Solution

$S P . S' P' = b^{2}; ∴ \sum_{i = 1}^{10} (S P_{i}) (S' P'_{i}) = 10 b^{2} = 2560 \Rightarrow b^{2} = 256 & a = 20 \Rightarrow e = \frac{3}{5}$

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