Mathematics | VITEEE 2018 | Discussion Page

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

Option C

Let a be the major axis and b, the minor axis of the ellipse, then 3 minor axis = major axis

→ 3b = a

Eccentricity is given by : b² = a²(1 - e²)

→ b² = 9b² (1 - e²)

$\frac{1}{9}= (1-e^{2})\Rightarrow e^{2}=\frac{8}{9}\Rightarrow e= \frac{2\sqrt{2}}{3}$

Discussion Forum