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Find the eccentricity of an ellipse (x^(...

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

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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))`
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