What is the length of the latus rectum of the parabola $x^2 - 4x - 8y + 12 = 0$?

The line $y = mx + 1$ is a tangent to the parabola $y^2 = 4x$,if

The length of the latus rectum of a parabola whose focal chord $PSQ$ is such that $PS = 3$ and $QS = 2$ is

What is the slope of the normal to the parabola $x^2 + 4y = 0$ at the point $(2, -1)$?

The parabola with directrix $x+2y-1=0$ and focus $(1,0)$ is

$S \equiv y^2 - 4ax = 0$ and $S' \equiv y^2 + ax = 0$ are two parabolas,and $P(t)$ is a point on the parabola $S' = 0$. If $A$ and $B$ are the feet of the perpendiculars from $P$ onto the coordinate axes and $AB$ is a tangent to the parabola $S = 0$ at the point $Q(t_1)$,then $t_1 =$