Find the equation of the parabola that satisfies the following conditions: Focus $(0, -3)$,directrix $y = 3$.

If $x + y = k$ is a normal to the parabola $y^2 = 12x$,then what is the value of $k$?

If the tangent to the parabola $4y^2 = x$ makes an angle of $60^{\circ}$ with the $x$-axis,then find its point of contact.

The point on the parabola $y^2 = 8x$ at which the normal is parallel to the line $x - 2y + 5 = 0$ is

The line $y=mx+1$ is a tangent to the curve $y^{2}=4x$ if the value of $m$ is

Let $P(4, -4)$ and $Q(9, 6)$ be two points on the parabola $y^2 = 4x$. Let $X$ be any point on the arc $POQ$ of this parabola,where $O$ is the vertex,such that the area of $\Delta PXQ$ is maximum. Then this maximum area (in sq. units) is