1.

If the distance between the foci of an ellipse is 8 and length of latus rectum is18/5, then the eccentricity of ellipse is:

Answer»

`2/5`
`3/5`
`4/5`
NONE of these

Solution :`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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