The equations of two ellipses are $\frac{x^2}{4}+\frac{y^2}{2}=1$ and $\frac{x^2}{36}+\frac{y^2}{\mathrm{~b}^2}=1$. If the product of their eccentricities is $\frac{\sqrt{2}}{3}$, then the product of the length of the major axis and minor axis of the second ellipse is

The eccentricity of the ellipse $9 x^2+5 y^2-30 y=0$ is

A rectangle of maximum area is inscribed in an ellipse $$\frac{x^2}{25}+\frac{y^2}{16}=1$$, then its dimensions are