Question

The eccentricity of the ellipse whose major axis is three times the minor axis is:

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

Answer 1

Answer: (C)

$\frac{2\sqrt{2}}{3}$

Answer 2

Let a be the major axis and b, the minor axis of the ellipse, then 3 minor axis = major axis. $\Rightarrow 3b = a$
Eccentricity is given by :
$b^{2} = a^{2}\left(1 - e^{2}\right)$
$\Rightarrow b^{2} = 9b^{2}\left(1 - e^{2}\right)$
$\Rightarrow \frac{1}{9} = \left(1 - e^{2}\right) \Rightarrow e^{2} = \frac{8}{9} \Rightarrow e = \frac{2\sqrt{2}}{3}$