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

Rajasthan PETRajasthan PET 2006

Solution:

Let major axis is o and minor axis is b. Given,
$ a=3b $ $ \therefore $ Eccentricity, $ e=\sqrt{1-\frac{{{b}^{2}}}{{{a}^{2}}}} $
$ \Rightarrow $ $ e=\sqrt{1-\frac{{{b}^{2}}}{9{{b}^{2}}}} $
$ \Rightarrow $ $ 3=\sqrt{\frac{9-1}{9}} $
$ =\frac{2\sqrt{2}}{3} $