The line $y = 2x + c$ is a tangent to the parabola $y^2 = 16x$,if $c$ equals

If the line $x - 1 = 0$ is the directrix of the parabola $y^2 - kx + 8 = 0$,then what is one value of $k$?

From the point $(-1, 2)$,tangent lines are drawn to the parabola $y^2 = 4x$. Find the equation of the chord of contact.

The length of the latus rectum of the parabola $20(x^2+y^2-6x-2y+10) = (4x-2y-5)^2$ is

From a point $(d, 0)$, three normals are drawn to the parabola $y^{2} = x$. Then:

Let $O$ be the vertex of the parabola $x^{2}=4y$ and $Q$ be any point on it. Let the locus of the point $P$, which divides the line segment $OQ$ internally in the ratio $2:3$, be the conic $C$. Then the equation of the chord of $C$, which is bisected at the point $(1, 2)$, is: