Mathematics | VITEEE 2018 | Discussion Page

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

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

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

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

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

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)

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

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