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 $(-1,-1)$ is the focus and $x+y+4=0$ is the directrix of a parabola,then its vertex is

If the line $y - \sqrt{3}x + 3 = 0$ cuts the parabola $y^2 = -x - 2$ at $A$ and $B$,then $PA \cdot PB$ is equal to,where $P \equiv (\sqrt{3}, 0)$.

The largest value of $k$ for which the circle $x^2+y^2=k^2$ lies completely in the interior of the parabola $y^2=4x+16$ is

The axis of the parabola $x^{2}+2 x y+y^{2}-5 x+5 y-5=0$ is

$P$ is a point on the parabola $y^2 = 4ax$ $(a > 0)$ whose vertex is $A$. $PA$ is produced to meet the directrix in $D$ and $M$ is the foot of the perpendicular from $P$ on the directrix. If a circle is described on $MD$ as a diameter,then it intersects the $x$-axis at a point whose coordinates are: