Let $P_i$ and $P'_i$ be the feet of perpendiculars drawn from foci $S$ and $S'$ on a tangent $T_i$ to the ellipse $E: \dfrac{x^2}{a^2} + \dfrac{y^2}{b^2} = 1$ whose length of major axis is 40 units.

If $\ \displaystyle \sum_{i=1}^{10} (SP_i)(SP'_i) = 2560$ , then find the value of $100e$ .

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' $e$ ' denotes the eccentricity of the ellipse.

The answer is 60.

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Simply use the property that product of length of perpendicular from the focii to any tangent is b^2

so b^2 = 256 b = 16 and a = 20

simply e = 3/5