At what points does the line $2x + y - 1 = 0$ intersect the parabola $y^2 = 4x$?

The locus of the midpoint of the line segment joining the focus to a moving point on the parabola $y^2 = 4ax$ is another parabola with the directrix

The directrix of the parabola ${x^2 - 4x - 8y + 12 = 0}$ is

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 $P$ is a point which divides the line segment joining the focus of the parabola $y^2=12x$ and a point on the parabola in the ratio $1:2$,then the locus of $P$ is:

Let $A, B$ and $C$ be three points on the parabola $y^2=6x$ and let the line segment $AB$ meet the line $L$ through $C$ parallel to the $x$-axis at the point $D$. Let $M$ and $N$ respectively be the feet of the perpendiculars from $A$ and $B$ on $L$. Then $\left(\frac{AM \cdot BN}{CD}\right)^2$ is equal to...........