The length of the latus rectum of the parabola ${x^2 - 4x - 8y + 12 = 0}$ is

The parametric equations $x - 2 = t^2$ and $y = 2t$ represent which parabola?

$AB$ is a chord of a parabola $y^2 = 4ax, (a > 0)$ with vertex $A$. $BC$ is drawn perpendicular to $AB$ meeting the axis at $C$. The projection of $BC$ on the axis of the parabola is

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

If a normal chord at a point $t$ on the parabola $y^2=4ax$ subtends a right angle at the vertex,then $t^2$ equals to

The equation of the common tangent drawn to the curves $y^2 = 8x$ and $xy = -1$ is