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Question

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


Correct Answer
A
512
Your Answer
B
5+12
 
Your Answer
C
514
 
Your Answer
D
none of these

Solution

The correct option is C 512
According to the question, the distance between the foci is equal to the length of the latus rectum 
2b2a=2ae
b2=a2e
Now, e=1b2a2
e=1a2ca2
e=1e
On squaring both sides, we get:
e2+e1=0
e=1±1+42
e=512    (ecannotbenegative)
 

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