What is the slope of the tangents drawn from $(3, 8)$ to the parabola $y^2 = -12x$?

If $(x_1, y_1)$ and $(x_2, y_2)$ are the end points of a focal chord of the parabola $y^2 = 5x$,then $4x_1x_2 + y_1y_2$ is equal to

If the normal at one end of the latus rectum of the parabola $y^2=16x$ meets the $X$-axis at the point $P$, then the length of the chord passing through $P$ and perpendicular to the normal is (in $\sqrt{2}$)

$P$ and $Q$ are the extremities of a focal chord of the parabola $y^2=4ax$. If $P=(9,9)$ and $Q=(p, q)$,then $p-q=$

The length of the latus rectum of the parabola ${y^2} - 4y - 2x - 8 = 0$ is

$A$ beam of light travels along the line $y = -4$ from right to left and strikes a parabola at point $P$. If the focus and directrix of the parabola are $(2, 0)$ and $x = -2$ respectively,then find the coordinates of the point where the reflected beam contacts the parabola again.