Gujarati
Hindi
10-2. Parabola, Ellipse, Hyperbola
normal

If end points of latus rectum of an ellipse are vertices of a square, then eccentricity of ellipse will be -

A

$\frac{1}{{\sqrt 2 }}$

B

$\frac{{\sqrt 5 \, + \,\,1}}{4}$

C

$\frac{{\sqrt 5 \, - \,\,1}}{4}$

D

$\frac{{\sqrt 5 \, - \,\,1}}{2}$

Solution

$ae$ $=\frac{b^{2}}{a} \Rightarrow 1-e^{2}=e $

$\Rightarrow e=\frac{\sqrt{5}-1}{2}$

Standard 11
Mathematics

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