# if the distance between the foci is equal to the length of the latus-rectum. Find the eccentricity of the ellipse.

$Distance\;between\;the\;foci\;of\;an\;ellipse=length\;of\;latus\;rectum\\* \Rightarrow \frac{2b^2}{a}=2ae\\*\Rightarrow e=\frac{b^2}{a^2}\\*\therefore e=\sqrt{1-\frac{b^2}{a^2}}=\sqrt{1-e}\\*Squaring\;both\;sides\;we\;get,\\* \Rightarrow e^2+e-1=0\\*\Rightarrow e=\frac{-1\pm\sqrt{1+4}}{-2}\\*\because e\;can\;not\;be\;negative\\*\therefore e=\frac{\sqrt5-1}{2}$

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