An ellipse has `O B` as the semi-minor axis, `Fa n dF '` as its foci, and `/_F B F '` a right angle. Then, find the eccentricity of the ellipse.

Options

A. `1/sqrt2`
B. `1/2`
C. `sqrt3/2`
D. none of these

Answer

A

Explanation

We have, `angleFBF' pi/2`
`therefore FF'^(2) = FB^(2) + F' B^(2)`
`rArr (2ae)^(2) = a^(2) + a^(2) [{:(because x - " coordinate of B is zero"),(therefore FB = a - e xx 0 and F' B = a + e xx 0):}]`
`rArr 4e^(2) = 2 rArr e = 1/sqrt2`