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  4. If the length of the major axis of an ellipse is three times the length of its minor axis, then its eccentricity is

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Q. If the length of the major axis of an ellipse is three times the length of its minor axis, then its eccentricity is

Conic Sections

Solution:

Given, major axis $=3$ (minor axis)
$ \Rightarrow 2 a=3(2 b) $
$ \Rightarrow a^2=9 b^2=9 a^2\left(1-e^2\right)$
$ \Rightarrow e=\frac{2 \sqrt{2}}{3}$