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If the eccentricity of the ellipse,x^2/(...

If the eccentricity of the ellipse,`x^2/(a^2+1)+y^2/(a^2+2)=1` is `1/sqrt6` then latus rectum of ellipse is

A

`5/sqrt(6)`

B

`10/sqrt(6)`

C

`8/sqrt(6)`

D

none of these

Text Solution

Verified by Experts

The correct Answer is:
B
Here , `a^(2)+2gta^(2)+1`
`:. a^(2)+1=(a^(2)+2)(1-e^(2))`
` or a^(2)+1=(a^(2)+2)(5)/(6)`
`or 6a^(2)+6=a^(2)+10`
`or a^(2)=10-6=4`
Latus reactum `=(2(a^(2)+1))/(sqrt(a^(2)+2))=(2xx5)/(sqrt(6))=(10)/(sqrt(6))`
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