The length of the latus rectum of the curve represented by $x=3(\cos t+\sin t)$ and $y=4(\cos t-\sin t)$ is:

The area of the region bounded by the ellipse $\frac{x^2}{a^2}+\frac{y^2}{b^2}=1$ is

The radius of the circle passes through the foci of a conic $\frac{x^2}{16}+\frac{y^2}{9}=1$ and has its centre at $(0,3)$, then the diameter of the circle is ---

If the distance between the foci is equal to the length of the latus rectum, then the eccentricity of the ellipse is