If $(2, k)$ is a point on the parabola passing through the points $(1, -3), (-1, 5), (0, 2)$ and having its axis parallel to the $Y$-axis,then $k$ is equal to

The distance of the point $(6, -2 \sqrt{2})$ from the common tangent $y = mx + c$ $(m > 0)$ of the curves $x = 2y^2$ and $x = 1 + y^2$ is

$P$ and $Q$ are the extremities of a focal chord of the parabola $y^2=4ax$. If $P=(9,9)$ and $Q=(p, q)$,then $p-q=$

If the ordinates of points $P$ and $Q$ on the parabola $y^2=12x$ are in the ratio $1:2$,then the locus of the point of intersection of the normals to the parabola at $P$ and $Q$ is

If all the vertices of an equilateral triangle lie on the parabola $y^2=16x$ and one of them coincides with the vertex of that parabola,then the length of the side of that triangle is

The locus of the vertices of the family of parabolas $y = \frac{a^3 x^2}{3} + \frac{a^2 x}{2} - 2a$ is