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

The point on the axis of the parabola $3y^2+4y-6x+8=0$ from which $3$ real normals can be drawn is given by:

Let $P(2,4)$ and $Q(18,-12)$ be the points on the parabola $y^2=8x$. The equation of the straight line having slope $\frac{1}{2}$ and passing through the point of intersection of the tangents to the parabola drawn at the points $P$ and $Q$ is

The focal distance of a point on the parabola $y^{2}=16x$ whose ordinate is twice the abscissa,is

If the normal at the point $t_1$ (i.e.,at $(at_1^2, 2at_1)$) on the parabola $y^2 = 4ax$ meets the parabola again at the point $t_2$,then $t_1t_2$ is equal to:

If $(2 t^2, 4 t)$ is a point on the parabola $y^2 = 8x$ such that its focal distance is $3$,then $t =$