An ellipse,with foci at $(0, 2)$ and $(0, -2)$ and minor axis of length $4$,passes through which of the following points?

If $P(\alpha, \beta)$ is a point on the curve $9x^2 + 4y^2 = 144$ in the first quadrant and the minimum area of the triangle formed by the tangent of the curve at $P$ with the coordinate axes is $S$,then

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.

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:

Let $x=4$ be a directrix to an ellipse whose centre is at the origin and its eccentricity is $\frac{1}{2}$. If $P(1, \beta), \beta>0$ is a point on this ellipse,then the equation of the normal to it at $P$ is

The line $x = 8$ is the directrix of the ellipse $E: \frac{x^2}{a^2} + \frac{y^2}{b^2} = 1$ with the corresponding focus $(2, 0)$. If the tangent to $E$ at the point $P$ in the first quadrant passes through the point $(0, 4\sqrt{3})$ and intersects the $x$-axis at $Q$,then $(3PQ)^2$ is equal to $........$