If $x + y = k$ is a normal to the parabola ${y^2} = 12x$,then $k$ is

If two parabolas $y^2 = 4x$ and $x^2 = 32y$ intersect at the point $(16, 8)$ at an angle $\theta$,then what is the value of $\tan \theta$?

If a normal chord at a point $t (\neq 0)$ on the parabola $y^2 = 9x$ subtends a right angle at its vertex,then $t =$

Let $x=2t, y=\frac{t^2}{3}$ be a conic. Let $S$ be the focus and $B$ be the point $(0, \alpha)$ on the axis of the conic such that $SA \perp BA$,where $A$ is any point $(2t, \frac{t^2}{3})$ on the conic. If $k$ is the ordinate of the centroid of $\Delta SAB$,then $\lim_{t \rightarrow 1} k$ is equal to

The focus and directrix of the parabola ${x^2} = - 8ay$ are

Let a circle tangent to the directrix of a parabola $y^2 = 2ax$ have its center coinciding with the focus of the parabola. Then the points of intersection of the parabola and the circle are