The eccentricity of the curve represented by $x=3(\cos t+\sin t), y=4(\cos t-\sin t)$ is

The foci of the conic $25 x^2+16 y^2-150 x=175$ are

AOB is the positive quadrant of the ellipse $\frac{x^2}{25}+\frac{y^2}{9}=1$ in which $\mathrm{OA}=5, \mathrm{OB}=3$. The area between the arc AB and the chord AB of the ellipse in sq. units is

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