If $(0, 0)$ is the vertex and $3x - 4y + 2 = 0$ is the directrix of a parabola,find the length of its latus rectum. (in $/5$)

Let a line $y=mx$ $(m>0)$ intersect the parabola $y^{2}=x$ at a point $P$,other than the origin. Let the tangent to it at $P$ meet the $x$-axis at the point $Q$. If $\text{area}(\Delta OPQ)=4$ sq. units,then $m$ is equal to

If the focal chord drawn through the point $(1,2)$ to the parabola $y^2=8x$ meets this parabola in $(x_1, y_1)$ and $(x_2, y_2)$,then $x_1+x_2=$

If a parabola having its axis parallel to the $X$-axis passes through the points $(0, -1)$,$(6, 1)$,and $(-2, -3)$,then the point at which this parabola cuts the $X$-axis is

If $x = t^2$ and $y = 2t$,then the equation of the normal at $t = 1$ is

The parametric equations of the parabola $y^2-4x-8y-12=0$ are