What is the equation of the chord of contact drawn from the point $(2, 4)$ to the parabola $y^2 = 4x$?

Tangents drawn from the point $(-8, 0)$ to the parabola $y^2 = 8x$ touch the parabola at $P$ and $Q$. If $F$ is the focus of the parabola,then the area of the triangle $PFQ$ (in sq. units) is equal to

The area of the triangle formed by the lines joining the vertex of the parabola $x^2=12y$ to the ends of its latus rectum is equal to $...$ sq. units.

If the parabola $y = \alpha x^{2} - 6x + \beta$ passes through the point $(0, 2)$ and has its tangent at $x = \frac{3}{2}$ parallel to the $X$-axis,then:

For the parabola $y^2 + 8x - 12y + 20 = 0$,which of the following is $NOT$ true?

Let $PQ$ be a focal chord of the parabola $y^2=36x$ of length $100$,making an acute angle with the positive $x$-axis. Let the ordinate of $P$ be positive and $M$ be the point on the line segment $PQ$ such that $PM:MQ=3:1$. Then which of the following points does $NOT$ lie on the line passing through $M$ and perpendicular to the line $PQ$?