The product of the lengths of perpendiculars from the foci on any tangent to the ellipse $3x^2 + 5y^2 = 1$ is:

The equation $\frac{x^2}{2 - r} + \frac{y^2}{r - 5} + 1 = 0$ represents an ellipse,if

The equation of the tangent at the point $(1/4, 1/4)$ of the ellipse $\frac{x^2}{4} + \frac{y^2}{12} = 1$ is

On the ellipse $4x^2 + 9y^2 = 1$,the points at which the tangents are parallel to the line $8x = 9y$ are

The minimum distance between two points $P$ and $Q$ on the ellipse $\frac{x^2}{25} + \frac{y^2}{4} = 1$,if the difference between the eccentric angles of $P$ and $Q$ is $\frac{3\pi}{2}$,is

The eccentricity of the ellipse $\frac{x^{2}}{36}+\frac{y^{2}}{16}=1$ is