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Q.

Let Pi and Pi' be the feet of the perpendicular drawn from the foci S and S' on a tangent Ti to an ellipse whose length of semi major axis is 20. If ∑i=110SPiS'Pi1=2560 , then the value of the eccentricity is

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a

12

b

25

c

35

d

45

answer is C.

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Detailed Solution

Product of length of perpendiculars from foci on a tangent to the ellipse=b2∴SP1S1P11=SP2S1P21=.........=SP10S1P101=b2∑i=110SPiS1Pi1=256010b2=2560⇒b2=256,⇒b=16b2= a2(1- e2)162=2021-e2⇒e=3/5

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