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

Step-by-step solution

aligned & Latus rectum = 2 b^2 a & minor axis =2 b & aligned 2 b^2 a & = 1 2 2 b b & = 2 b^2 a a & =2 b aligned aligned Now from formula b^2=a^2 (1-e^2 ) aligned b^2 & =4 b^2 (1-e^2 ) 1 4 & =1-e^2 e^2 & =1- 1 4 e^2 & = 3 4 e & = 3 2 aligned