Question

Find the eccentricity of an ellipse `(x^2)/(a^2)+(y^2)/(b^2)=1` whose latus rectum is half of its major axis.

Answer 1

Let `agtb`.
Then the latus reactum of ellipse is `(2b^(2))/(a)`
Given that `(2b^(2))/(a)=a`
`rArrr (b^(2))/(a^(2))=(1)/(2)`
`:. E^(2)=1-(b^(2))/(a^(2))=1-(1)/(2)=(1)/(2)`
`:. e=(1)/(sqrt(2))`