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Let Pi and Pi ' be the feet of the perpe...

Let `P_i` and `Pi '` be the feet of the perpendiculars drawn from the foci `Sa n dS '` on a tangent `T_i` to an ellipse whose length of semi-major axis is 20. If `sum_(i=0)^(10)(S P_i)(S^(prime)Pi ')=2560 ,` then the value of eccentricity is `1/5` (b) `2/5` (c) `3/5` (d) `4/5`

Text Solution

Verified by Experts

Equation of ellipse can be given as
`x^2/a^2+y^2/b^2 = 1`
Here, Foci of ellipse `= (0+-5)`
This mean, the major axis is Y-axis and `c = 5`.
Length of major axis ` = 20`
`=> 2b = 20=> b = 10`
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