If the length of the major axis of an ellipse | vedclass

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(D) Let the length of the major axis be $2a$ and the length of the minor axis be $2b$.Given that the length of the major axis is three times the lengt

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

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(D) Let the length of the major axis be $2a$ and the length of the minor axis be $2b$.Given that the length of the major axis is three times the length of the minor axis:$2a = 3(2b) \implies a = 3b$.We know the formula for eccentricity $e$ of an ellipse is $e = \sqrt{1 - \frac{b^2}{a^2}}$.Substituting $a = 3b$ into the formula:$e = \sqrt{1 - \frac{b^2}{(3b)^2}}$$e = \sqrt{1 - \frac{b^2}{9b^2}}$$e = \sqrt{1 - \frac{1}{9}}$$e = \sqrt{\frac{8}{9}}$$e = \frac{\sqrt{8}}{3} = \frac{2\sqrt{2}}{3}$.Thus,the eccentricity is $\frac{2\sqrt{2}}{3}$.

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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