For the parabola $y^2 = 8x$,what is the position of the point $(2, 5)$?

Let one end of a focal chord of the parabola $y^{2}=16x$ be $(16, 16)$. If $P(\alpha, \beta)$ divides this focal chord internally in the ratio $5 : 2$,then the minimum value of $\alpha+\beta$ is equal to:

Find the length of the latus rectum of a parabola if $PSQ$ is a focal chord such that $SP = 3$ and $SQ = 2$.

The locus of the mid-point of the line segment joining the focus and any point on the parabola $y^{2}=4ax$ is a parabola. Find the equation of its directrix.

If a parabola passes through the points $(-2, 1)$,$(1, 2)$,and $(-1, 3)$ and has a horizontal axis,then the length of the latus rectum of that parabola is:

$A$ circle of radius $4$,drawn on a chord of the parabola $y^2 = 8x$ as diameter,touches the axis of the parabola. Then,the slope of the chord is