If $P \equiv (x, y)$,$F_1 \equiv (3, 0)$,$F_2 \equiv (-3, 0)$ and $16x^2 + 25y^2 = 400$,then $PF_1 + PF_2$ equals

If $y = mx + c$ is a tangent to the ellipse $\frac{x^2}{9} + \frac{y^2}{4} = 1$,then the value of $c$ is ...

An ellipse is drawn such that the diameter of the circle $(x - 1)^2 + y^2 = 1$ is the semi-minor axis and the diameter of the circle $x^2 + (y - 2)^2 = 4$ is the semi-major axis. If the center of the ellipse is at the origin and its axes are the coordinate axes,find the equation of the ellipse.

$A$ focus of an ellipse having eccentricity $e = \frac{1}{2}$ is at $(0,0)$ and a directrix is the line $x = 4$. Then the equation of one such ellipse is

If the line $x \cos \alpha + y \sin \alpha = p$ is normal to the ellipse $\frac{x^2}{a^2} + \frac{y^2}{b^2} = 1$,then

If $\theta$ is the eccentric angle of a point on the ellipse $\frac{x^2}{25} + \frac{y^2}{9} = 1$ such that the distance of the point from the center is $5$, then $\theta = ......$