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

Let `P_i` and `P_i '` 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 (a) `1/5` (b) `2/5` (c) `3/5` (d) `4/5`

A

`1//5`

B

`2//5`

C

`3//5`

D

`4//5`

Text Solution

Verified by Experts

`underset(i=i)overset(10)sum(SP_(i))(S'P_(i))=2560`
or `10b^(2)=2560`
`or b^(2)=256`
or b=16
Now, `256=400(1-e^(2))`
or `1-e^(2)=(16)/(25)`
`e=(3)/(5)`
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