Tangents are drawn from points on the circle $x^2 + y^2 = 49$ to the ellipse $\frac{x^2}{25} + \frac{y^2}{24} = 1$. The angle between the tangents is:

$A$ point on the curve $x=3 \cos \theta, y=2 \sin \theta$ at which the tangent is perpendicular to the $X$-axis is

Let a tangent drawn at any point on the ellipse $\frac{x^2}{25}+\frac{y^2}{16}=1$ cut the $X$-axis at $Q$. Let $R$ be the image of $Q$ with respect to $y=x$. If $S$ is a circle with $QR$ as its diameter,then the fixed point through which the circle $S$ passes is

Tangent to the ellipse $\frac{x^{2}}{32}+\frac{y^{2}}{18}=1$ having slope $-\frac{3}{4}$ meets the coordinate axes at $A$ and $B$. Find the area of the $\Delta AOB$,where $O$ is the origin.

The foci of the ellipse $25x^2 + 4y^2 + 100x - 4y + 100 = 0$ are

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