Question

If the length of the major axis of a vertical ellipse is three times length of 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,
$2b=3\left(2a\right)\Rightarrow b=3a\Rightarrow b^2=9a^2\Rightarrow \frac{a^2}{b^2}=\frac{1}{9}\Rightarrow e^2=\frac{8}{9}\therefore e=\frac{2\sqrt{2}}{3}$