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If the line joining foci subtends an ang...

If the line joining foci subtends an angle of `90^(@)` at an extremity of minor axis, then the eccentricity e is

A

`(1)/(sqrt(6))`

B

`(1)/(sqrt(3))`

C

`(1)/(sqrt(2))`

D

`(1)/(2sqrt(2))`

Text Solution

Verified by Experts

The correct Answer is:
C

`:.F_(1)B bot F_(2)B`
`rArr m_(1)m_(2)= -1`
`rArr (b-0)/(0-ae) xx (b-0)/(0+a e) = -1`
`rArr (b^(2))/(a^(2)e^(2))=1`
`rArr 2e^(2)=1`
`rArr e^(2)=(1)/(2)`
`rArr e=(1)/(sqrt(2))`
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