The ratio of the ordinates of a point and its corresponding point is$\frac{2\sqrt{2}}{3}$then eccentricity is

$\begin{array}{l}\mathrm{let} \mathrm{P}=(\mathrm{acos}\mathrm{\theta },\mathrm{bsin}\mathrm{\theta }) be any point on ellipse and its corresponding point be {\mathrm{P}}^{\mathrm{\prime }}(\mathrm{acos}\mathrm{\theta },\mathrm{asin}\mathrm{\theta })\\ \frac{\mathrm{b}}{\mathrm{a}}=\frac{2\sqrt{2}}{3}\\ \Rightarrow \frac{b^2}{a^2}=\frac{8}{9}\\ \Rightarrow 1-e^2=\frac{8}{9}\\ \Rightarrow e=\frac{1}{3}\end{array}$