Question

If the major axis is “n” (n>1) times the minor axis of the ellipse, then its eccentricity is

• A.
• B.
• C.
• D.

Answer 1

The correct option is D

$2a=n\left(2b\right)$
$\Rightarrow n=\frac{a}{b}$
$\therefore e=\sqrt{\frac{a^2-b^2}{a^2}}=\sqrt{1-\frac{b^2}{a^2}}=$
$\sqrt{1-\frac{1}{n^2}}=\frac{\sqrt{n^2-1}}{n}$