How many parabolas can be drawn if the endpoints of the latus rectum are given?

$TP$ and $TQ$ are tangents to the parabola $y^2 = 4ax$ at $P$ and $Q$. If the chord $PQ$ passes through the fixed point $(-a, b)$,then the locus of $T$ is:

If the points of intersection of two distinct conics $x^2+y^2=4b$ and $\frac{x^2}{16}+\frac{y^2}{b^2}=1$ lie on the curve $y^2=3x^2$,then $3\sqrt{3}$ times the area of the rectangle formed by the intersection points is............................

The locus of the foot of the perpendicular drawn from the centre upon any tangent to the ellipse $\frac{x^2}{a^2} + \frac{y^2}{b^2} = 1$ is

Tangents are drawn from the point $P\ (3, 4)$ to the ellipse $\frac{x^2}{9} + \frac{y^2}{4} = 1$,touching the ellipse at points $A$ and $B$. Find the coordinates of $A$ and $B$.

Tangents are drawn from the point $P(3, 4)$ to the ellipse $\frac{x^2}{9} + \frac{y^2}{4} = 1$,touching the ellipse at points $A$ and $B$. The orthocenter of $\Delta PAB$ is: