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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 =8implies ae =4, implies a ^(2) = b ^(2) + 16`
Length of L.R.` (2b^(2))/(a) = (18)/(5) implies b^(2) = 9/5 a`
`implies a ^(2) = (99)/(5) + 16 implies 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 implies e = 4/5`
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