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

Given that we need to find the eccentricity of the ellipse whose latus - rectum is equal to the distance between the foci.


We know that length of latus rectum is and distance between foci is 2ae.



b2 = a2e.


We know that eccentricity of the ellipse is b2 = a2(1 - e2)


a2(1 - e2) = a2e


e2 + e - 1 = 0



(since e>0)


The correct option is A

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