The equations of the directrices of the ellipse $9x^2 + 4y^2 - 18x - 16y - 11 = 0$ are

Tangents are drawn to the ellipse $\frac{x^2}{25}+\frac{y^2}{16}=1$ at all the four ends of its latus rectum. The area (in sq units) of the quadrilateral formed by these tangents is

$S$ and $T$ are the foci of an ellipse and $B$ is the end point of the minor axis. If $\triangle STB$ is an equilateral triangle,the eccentricity of the ellipse is

If the lines joining the foci of the ellipse $\frac{x^2}{a^2} + \frac{y^2}{b^2} = 1$ (where $a > b$) to an extremity of its minor axis are inclined at an angle of $60^{\circ}$ to each other,then the eccentricity of the ellipse is:

If tangents are drawn from any point on the circle $x^2+y^2=25$ to the ellipse $\frac{x^2}{16}+\frac{y^2}{9}=1$,then the angle between the tangents is

At which points on the ellipse $4x^2 + 9y^2 = 1$ is the tangent line parallel to the line $8x = 9y$?