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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