Question

If the major axis is "n” times the minor axis of the ellipse, then its eccentricity is

• A. $\frac{\sqrt{n-1}}{n}$
• B. $\frac{\sqrt{n-1}}{n^2}$
• C. $\frac{\sqrt{n^2-1}}{n^2}$
• D. $\frac{\sqrt{n^2-1}}{n}$

Answer 1

The correct option is D

$\frac{\sqrt{n^2-1}}{n}$

a= nb $\to$ $\frac{b}{a}$ = $\frac{1}{n}$

e = $\sqrt{1-\frac{b^2}{a^2}}$ = $\sqrt{1-\frac{1}{n^2}}$ = $\sqrt{\frac{n^2-1}{n^2}}$