For any non-zero real value of $m$,the equation of the parabola to which the line $m x-y+10+m^2=0$ is a tangent,is

Find the coordinates of the point on the parabola $y^2 = 8x$ whose focal distance is $4$.

Let $x+y=k$ be a normal to the parabola $y^2=12x$. If $p$ is the length of the perpendicular from the focus of the parabola onto this normal,then $4k-2p^2$ is equal to

If the normals at two points $P$ and $Q$ of a parabola $y^2 = 4ax$ intersect at a third point $R$ on the curve,then the product of the ordinates of $P$ and $Q$ is (in $a^2$)

If the line $2x + 3y + n = 0$ is a tangent to the parabola $y^2 = 8x$,then the equation of the normal drawn at the point $(2n, 4\sqrt{n})$ to the parabola $y^2 = 8x$ is

Let $O$ be the vertex and $Q$ be any point on the parabola $x^2=8y$. If the point $P$ divides the line segment $OQ$ internally in the ratio $1:3$, then the locus of $P$ is