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

$A$ circle has its center $C$ on the axis of a parabola and it touches the parabola at point $P$. The line segment $CP$ makes an angle of $120^{\circ}$ with the axis of the parabola. If the radius of the circle is $2$,then the latus rectum of the parabola is:

If two circles $x^2+y^2-6x-6y+13=0$ and $x^2+y^2-8y+9=0$ intersect at $A$ and $B$,then the focus of the parabola whose directrix is the line $AB$ and vertex is the point $O(0,0)$ is

Find the equation of the common tangent to the parabolas $y^2 = 2x$ and $x^2 = 16y$.

Two tangent lines $l_{1}$ and $l_{2}$ are drawn from the point $(2,0)$ to the parabola $2y^{2} = -x$. If the lines $l_{1}$ and $l_{2}$ are also tangent to the circle $(x-5)^{2} + y^{2} = r$,then $17r$ is equal to.

The vertex of a parabola is $(2, 2)$ and the coordinates of the two extremities of its latus rectum are $(-2, 0)$ and $(6, 0)$. The equation of the parabola is