The tangents drawn at the extremities of a focal chord of the parabola $y^{2}=16x$:

If a chord of the parabola $y^2=4x$ passes through its focus and makes an angle $\theta$ with the $X$-axis,then its length is

If the focus of a parabola divides a focal chord of the parabola into segments of lengths $5$ and $3$ units,then the length of the latus rectum of that parabola is:

If the vertex of the conic $y^{2}-4y=4x-4a$ always lies between the straight lines $x+y=3$ and $2x+2y-1=0$,then:

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 $PQ$?

The focus of a parabolic mirror as shown in the figure is at a distance of $5 \, cm$ from its vertex. If the mirror is $45 \, cm$ deep,find the distance $AB$. (in $, cm$)