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

Let $P$ be a point on the parabola $y^2 = 4ax$,where $a > 0$. The normal to the parabola at $P$ meets the $x$-axis at a point $Q$. The area of the triangle $PFQ$,where $F$ is the focus of the parabola,is $120$. If the slope $m$ of the normal and $a$ are both positive integers,then the pair $(a, m)$ is

The equation of the tangent to the parabola $y^2=16x$,which is perpendicular to the line $3x-4y+5=0$,is given by

The line $x-2y-3=0$ cuts the parabola $y^2=4ax$ at the points $P$ and $Q$. If the focus of this parabola is $(\frac{1}{4}, k)$,then $PQ=$

The $Y$-intercept of the common tangent to the parabola $y^2 = 32x$ and $x^2 = 108y$ is

If $(0, 6)$ and $(0, 3)$ are respectively the vertex and focus of a parabola,then its equation is