Question

The distance between the foci of an ellipse is equal to the length of latusrectum. Its eccentricity is

• A. $\frac{1}{2\sqrt{2}}$
• B. $\frac{2\sqrt{2}}{3}$
• C. $\frac{\sqrt{5}-1}{2}$
• D. $\frac{\sqrt{3}-1}{2}$

Answer 1

The correct option is C $\frac{\sqrt{5}-1}{2}$

Given,

$2ae=\frac{2b^2}{a}$..................(using the relation of a,b and e)

$ae=\frac{a^2(1-e^2)}{a}$

$e=1-e^2$

$e^2+e-1=0$

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