Question

If the latus - rectum of an ellipse is one half of its minor axis, then its eccentricity is

A. 1/2

B. 1/√2

C. √3/2

D. √3/4

Answer 1

Correct option is C. √3/2

Given that we need to find the eccentricity of the ellipse whose latus - rectum is one half of the minor axis. We know that length of latus rectum \(\cfrac{2b^2}a\) is and length of minor axis is 2b.

⇒ \(\cfrac{2b^2}a=b\)

⇒ a = 2b.

We know that eccentricity of the ellipse is