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If the distance between the foci of an e...

If the distance between the foci of an ellipse is 8 and length of latus rectum is `18/5,` then the eccentricity of ellipse is:

A

`2/5`

B

`3/5`

C

`4/5`

D

None of these

Text Solution

Verified by Experts

The correct Answer is:
C
`2ae=8 rArr ae=4 , b^2=a^2(1-e^2)`
`rArr b^2=a^2-(ae)^2 rArr a^2=b^2+16`
Length of L.R. `(2b^2)/a = 18/5 rArr b^2=9/5a`
`rArr a^2=99/5 + 16 rArr 5a^2-99-80=0`
`5a^2-25a+16a-80=0`
`5a(a-5)+16(a-5)=0`
(a-5)(5a+16)=0
`a=5 rArr e=4/5`
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