If the normal to the parabola $y^2 = 4ax$ intersects the axis of the parabola at a distance of $4a$ from the vertex,then the slopes of the normal are in which progression?

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

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

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

Tangent and normal are drawn at $P(16, 16)$ on the parabola ${y^2} = 16x$,which intersect the axis of the parabola at $A$ and $B$,respectively. If $C$ is the centre of the circle through the points $P, A$ and $B$ and $\angle CPB = \theta$,then a value of $\tan \theta$ is:

Let $PQ$ be a chord of the parabola $y^2=12x$ and the midpoint of $PQ$ be at $(4,1)$. Then,which of the following points lies on the line passing through the points $P$ and $Q$?