The eccentricity of the ellipse if the distance between the foci is equal to the length of the latusrectum ,is

Options

A. `(sqrt(5)-1)/(2)`
B. `(sqrt(5)+1)/(4)`
C. `(sqrt(5)-1)/(4)`
D. none of these

Answer

A

Explanation

we have ,
`2ae=(2b^(2))/(a)implies a^(2)e =b^(2)implies a^(2)e=a^(2)(1-e^(2))`
`implies e^(2)+e-1=0implies r=(sqrt(5)-1)/(2)`