Let `L L '` be the latus rectum through the focus of the hyperbola `(x^2)/(a^2)-(y^2)/(b^2)=1` and `A '` be the farther vertex. If ` A ' L L '` is equilateral, then the eccentricity of the hyperbola is (axes are coordinate axes). `sqrt(3)` (b) `sqrt(3)+1` `((sqrt(3)+1)/(sqrt(2)))` (d) `((sqrt(3)+1))/(sqrt(3))`

Options

A. `sqrt3`
B. `sqrt3+1`
C. `(sqrt3+1)//sqrt2`
D. `(sqrt3+1)//sqrt3`

Answer

D

Explanation

`tan30^(@)=(b^(2))/(a+ae)`
`"or "(1+e)/(sqrt3)=e^(2)-1`
`"or "e-1=(1)/(sqrt3)`
`"or "e=(sqrt3+1)/(sqrt3)`