If the distance between the foci of an ellips | vedclass

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Question

Focus of an ellipse is given as $\left( { \pm ae,0} \right)$

distance between then $=2ae$

According to the quation, $2ae = \frac{{{b^2

Vedclass · Accepted Answer

$\sqrt 2  - 1$

Vedclass · Answer

Focus of an ellipse is given as $\left( { \pm ae,0} \right)$

distance between then $=2ae$

According to the quation, $2ae = \frac{{{b^2}}}{a}$

$ \Rightarrow 2{a^2}e = {b^2} = {a^2}\left( {1 - {e^2}} \right)$

$ \Rightarrow 2e = 1 - {e^2} \Rightarrow {\left( {e - 1} \right)^2} = 2 \Rightarrow e = \sqrt 2  - 1$

If the distance between the foci of an ellipse is half the length of its latus rectum, then the eccentricity of the ellipse is

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