Which of the following points lie on the parabola $x^2 = 4ay$?

The length of the latus rectum of the parabola $9x^2 - 6x + 36y + 19 = 0$ is:

Statement $I$: $4x^2+y^2-4xy-30x-50y+40=0$ is the equation of a parabola having $(2,3)$ as its focus and $x+2y+5=0$ as its directrix.
Statement $II$: The equation of the directrix of the parabola $x^2-4x+16y+52=0$ is $y+1=0$.
Which of the above statements is (are) true?

The point of contact of the tangent $18x - 6y + 1 = 0$ to the parabola $y^2 = 2x$ is

Find the axis of the parabola $9y^2 - 16x - 12y - 57 = 0$.

$P$ 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: