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(C) Let the equation of the ellipse be $\frac{x^2}{a^2} + \frac{y^2}{b^2} = 1$,where $b > a$.The length of the latus rectum is $\frac{2a^2}{b}$ and th

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$\frac{\sqrt{5}}{3}$

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(C) Let the equation of the ellipse be $\frac{x^2}{a^2} + \frac{y^2}{b^2} = 1$,where $b > a$.The length of the latus rectum is $\frac{2a^2}{b}$ and the length of the minor axis is $2a$.Given that the length of the latus rectum is $\frac{2}{3}$ times the length of the minor axis:$\frac{2a^2}{b} = \frac{2}{3}(2a)$$\frac{a^2}{b} = \frac{2a}{3}$$\frac{a}{b} = \frac{2}{3}$$\frac{a^2}{b^2} = \frac{4}{9}$The eccentricity $e$ is given by $e = \sqrt{1 - \frac{a^2}{b^2}}$.$e = \sqrt{1 - \frac{4}{9}} = \sqrt{\frac{5}{9}} = \frac{\sqrt{5}}{3}$.

An ellipse has its major axis along the $y$-axis and its minor axis along the $x$-axis. If the length of its latus rectum is $\frac{2}{3}$ times the length of its minor axis,then the eccentricity of the ellipse is:

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