If the length of the major axis is n times the minor axis of the ellipse, then ecccentricity is

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$\frac{\sqrt{n - 1}}{n}$

$\frac{\sqrt{n - 1}}{n^{2}}$

$\frac{\sqrt{n^{2} - 1}}{n^{2}}$

$\frac{\sqrt{n^{2} - 1}}{n}$

answer is D.

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Detailed Solution

$\begin{array}{l} {AA}^{'} = {nBB}^{'} \Rightarrow a = nb \\ \Rightarrow e = \sqrt{\frac{a^{2} - b^{2}}{a^{2}}} \\ \Rightarrow e = \sqrt{\frac{n^{2} b^{2} - b^{2}}{n^{2} b^{2}}} = \sqrt{\frac{n^{2} - 1}{n^{2}}} \end{array}$

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