The equation of the parabola with its vertex at the origin,axis on the $y$-axis and passing through the point $(6, -3)$ is

$TP$ and $TQ$ are tangents of the parabola $y^2 = 8x$ at $P$ and $Q$ respectively. If the chord $PQ$ passes through the point $(-2, 3)$ and the locus of point $T$ is $y = mx + c$,then $(m + c)$ is equal to -

What is the area of the triangle formed by the vertex of the parabola $x^2 = 12y$ and the endpoints of its latus rectum (in square units)?

What is the vertex of the parabola $9x^2 - 6x + 36y + 9 = 0$?

What are the parametric equations of the parabola $(y - 2)^2 = 12(x - 4)$?

The area (in sq. units) of an equilateral triangle inscribed in the parabola $y^{2}=8x$, with one of its vertices at the vertex of this parabola, is (in $\sqrt{3}$)