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

For the parabola $y^2 = x$,let $PQ$ be a chord such that one endpoint $P$ is $(4, -2)$ and the chord is perpendicular to the axis of the parabola. What is the slope of the normal at $Q$?

Tangents drawn from the point $(-8, 0)$ to the parabola $y^2 = 8x$ touch the parabola at $P$ and $Q$. If $F$ is the focus of the parabola,then the area of the triangle $PFQ$ (in sq. units) is equal to

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

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

Find the coordinates of the focus,axis of the parabola,the equation of the directrix,and the length of the latus rectum for $y^{2} = -8x$.