The eccentricity of the ellipse, if the distance between the foci is equal to the lenght of the latus rectum, is

Explanation

`frac{2 b^{2}}{a}=2ae`

`Rightarrow e=frac{b^{2}}{a^{2}}`

But `e=sqrt{1-frac{b^{2}}{a^{2}}}`

`e=sqrt{1-e}`

Squaring both sides

`e^{2}+e-1=0 `

`Rightarrow e=frac{-1 pm sqrt{1+4}}{2}`(`therefore` Ecentricity cannot be negative )

`Rightarrow e=frac{sqrt{5}-1}{2}`
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