The line $x - y + 2 = 0$ touches the parabola $y^2 = 8x$ at the point

If the line $lx + my + n = 0$ is tangent to the parabola $y^{2} = 4ax$,then

What is the polar of the focus of a parabola?

If ${y_1}$ and ${y_2}$ are the ordinates of two points $P$ and $Q$ on the parabola ${y^2 = 4ax}$ and ${y_3}$ is the ordinate of the point of intersection of the tangents at $P$ and $Q$,then:

Let $O$ be the origin and $A$ be a point on the curve $y^2=4x$. Then the locus of the midpoint of $OA$ is:

The equation of the tangent to the parabola $y = (x - 3)^2$ parallel to the chord joining the points $(3, 0)$ and $(4, 1)$ is: