Question

If the major axis of a vertical ellipse is three times the minor axis, then its eccentricity is equal to

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

Answer 1

The correct option is C $\frac{2\sqrt{2}}{3}$

For vertical ellipse,
Length of the major axis $=2b$
Length of the minor axis $=2a$
Given,
$2b=3\left(2a\right)$
$\Rightarrow b=3a$
$\Rightarrow b^2=9a^2$
$\Rightarrow b^2=9b^2(1-e^2)\Rightarrow e^2=\frac{8}{9}$
$\Rightarrow e=\frac{2\sqrt{2}}{3}$