If the latus rectum of an ellipse is equal to half of the minor axis, then what is its eccentricity?

Step-by-step solution

aligned 2 b^2 a & =b 2 b & =a b^2 & =a^2 (1-e^2 ) b^2 & =4 b^2 (1-e^2 ) 1 4 & =1-e^2 e^2 & =1- 1 4 = 3 4 e & = 3 2 . aligned