The vertex of the parabola $y^2 + 2y + x = 0$ lies in which quadrant?

If a focal chord of the parabola $y^2 = 4ax$ makes an angle $\theta$ with its axis,then the length of the perpendicular from the vertex to this chord is......

Let $M$ be the foot of the perpendicular from a point $P$ on the parabola $y^2=8(x-3)$ onto its directrix and let $S$ be the focus of the parabola. If $\triangle SPM$ is an equilateral triangle,then $P$ is equal to

Let $O$ be the vertex of the parabola $y^2 = 4x$ and its chords $OP$ and $OQ$ are perpendicular to each other. If the locus of the mid-point of the line segment $PQ$ is a conic $C$,then the length of its latus rectum is:

The directrix of the parabola $2 y^2+25 x=0$ is $........$

For the parabola $y^2+6y-2x=-5$,consider the following statements:
$I$. The vertex is $(-2, -3)$.
$II$. The directrix is $y+3=0$.
Which of the following is correct?