The vertex of the parabola $x^2 + 4x + 2y - 7 = 0$ is

Two tangents are drawn from a point $(-2, -1)$ to the curve $y^2 = 4x$. If $\alpha$ is the angle between them,then $|\tan \alpha|$ is equal to:

$P$ and $Q$ are two points on the parabola $y^2 = 8x$ and $S$ is its focus. $PS$ and $QS$ meet the curve again in $T$ and $R$ respectively. If $PQ$ passes through a fixed point $(-2, 3)$,then $TR$ also passes through a fixed point whose coordinates are

The locus of the poles of focal chords of a parabola is:

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 $\sqrt{2}$)

The area of the triangle formed by the lines joining the vertex of the parabola $x^2 = 12y$ to the ends of its latus rectum is .................. $sq. \ unit$.