If the tangent drawn at the point $P(4,8)$ to the parabola $y^2=16 x$ meets the parabola $y^2=16 x+80$ at $A$ and $B$, then the mid-point of $A B$ is

For the parabola $y=\frac{h^3}{3} x^2+\frac{h^2}{2} x-h+\frac{3}{4 h^3}$, if the equation of directrix is $y=k$, then $k: h$

The equation of the common tangent of the parabolas $x^2=108 y$ and $y^2=32 x$ is

Consider the parabola $y^2+2 x+2 y-3=0$ and match the items of List-I with those of the List-II.

$$ \begin{array}{llll} \hline & \text { List-I } & & \text { List-II } \\ \hline \text { A. } & 2 x-5=0 & \text { I. } & \text { Vertex } \\ \hline \text { B. } & \left(\frac{3}{2},-1\right) & \text { II. } & \text { Focus } \\ \hline \text { C. } & y+1=0 & \text { III. } & \text { Equation of directrix } \\ \hline \text { D. } & (2,-1) & \text { IV. } & \text { Equation of the axis } \\ \hline & & \text { V. } & \text { Equation of the Latus rectum } \\ \hline \end{array} $$