For the parabola $y=x^2-3 x+2$, match the items in List I to that of the items in List II. $S$ is a focus, $Z$ is intersection of axis and directrix, $P$ is one end of latus rectum, $Q$ is the point on the parabola at which tangent is parallel to $X$-axis.

$$ \begin{array}{llll} \hline & \text { List I } & & \text { List II } \\ \hline \text { A. } & P & \text { I. } & (2,0) \\ \hline \text { B. } & Q & \text { II. } & \left(\frac{3}{2},-\frac{1}{4}\right) \\ \hline \text { C. } & S & \text { III. } & \left(\frac{3}{2}, 0\right) \\ \hline \text { D. } & Z & \text { IV. } & \left(\frac{3}{2},-\frac{1}{2}\right) \\ \hline & & \text { V. } & \left(0, \frac{3}{2}\right) \\ \hline \end{array} $$

The locus of a point which divides the line segment joining the focus and any point on the parabola $y^2=12 x$ in the ratio $m: n(m+n \neq 0)$ is a parabola.

Then, the length of the latus rectum of that parabola is

If the normal drawn at $P(8,16)$ to the parabola $y^2=32 x$ meets the parabola again at $Q$, then the equation of the tangent drawn at $Q$ to the parabola is

The focal distance of a point $(5,5)$ on the parabola $x^2-2 x-4 y+5=0$ is