If $\frac{\sqrt{3}}{a}x + \frac{1}{b}y = 2$ touches the ellipse $\frac{x^2}{a^2} + \frac{y^2}{b^2} = 1$,then its eccentric angle $\theta$ is equal to: ................ $^o$

If the points of intersection of the ellipse $\frac{x^{2}}{16}+\frac{y^{2}}{b^{2}}=1$ and the circle $x^{2}+y^{2}=4b$ (where $b > 4$) lie on the curve $y^{2}=3x^{2}$,then $b$ is equal to:

If $\theta$ and $\phi$ are eccentric angles of the ends of a pair of conjugate diameters of the ellipse $\frac{x^2}{a^2} + \frac{y^2}{b^2} = 1$,then $\theta - \phi$ is equal to

Let the length of the latus rectum of an ellipse with its major axis along the $x$-axis and center at the origin be $8$. If the distance between the foci of this ellipse is equal to the length of its minor axis,then which one of the following points lies on it?

If the length of the latus rectum of the ellipse $x^{2} + 4y^{2} + 2x + 8y - \lambda = 0$ is $4$,and $l$ is the length of its major axis,then $\lambda + l$ is equal to $......$

The radius of the circle passing through the foci of the ellipse $\frac{x^2}{16} + \frac{y^2}{9} = 1$ and having its center at $(0, 3)$ is: