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If the latus rectum of an ellipse is equ...

If the latus rectum of an ellipse is equal to the half of minor axis, then find its eccentricity.

A

`1/2`

B

`sqrt3/2`

C

`3/4`

D

`sqrt(15)/4`

Text Solution

Verified by Experts

The correct Answer is:
B
Length of latus rectum of an ellipse is `(2b^(2))/a` whereb is semi minor axis. As given , `(2b^(2))/a=b`
`rArr" "2b=arArrb/a=1/2`
`"We know that occentricitye "=sqrt(1-b^(2)/a^(2))=sqrt(1-1/4)=sqrt3/2`
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