Question

# The eccentricity of the ellipse, if the distance between the foci is equal to the length of the latus-rectum, is

A
512
B
5+12

C
514

D
none of these

Solution

## The correct option is C √5−12According to the question, the distance between the foci is equal to the length of the latus rectum  2b2a=2ae ⇒b2=a2e Now, e=√1−b2a2 ⇒e=√1−a2ca2 ⇒e=√1−e On squaring both sides, we get: e2+e−1=0 ⇒e=−1±√1+42 ⇒e=√5−12    (∵ecannotbenegative)

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