The pole of the line $lx + my + n = 0$ with respect to the parabola $y^{2} = 4ax$ is

The equations $x = \frac{t}{4}$ and $y = \frac{t^2}{4}$ represent:

Find the area of the triangle formed by the tangent and the normal at one end of the latus rectum of the parabola $y^2 = 4ax$ with the axis of the parabola.

The locus of the middle points of all chords of the parabola $y^2 = 4ax$ passing through the vertex is

Find the equation of the tangent to the curve $y^2 = 6x$ at the point $(2, -3)$.

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 $PQ$?