Question

Find the eccentricity of an ellipse, if the length of its latus rectum is one-third of its minor axis.

Answer 1

   Let the required equation of ellipse be \(\frac {x^2}{a^2} + \frac {y^2}{b^2} = 1\) where a > b.

Length of latus rectum = 2b²/a

Length of minor axis = 2b 

According to the given condition,

Length of latus rectum = 1/3 (Minor axis)