The equations of common tangents to the parabola $y^2=16 x$ and the circle $x^2+y^2=8$ are

The equation of the given curve is $x^2-4 x+4 y-8=0$. Match the following

$$ \begin{array}{lll} \hline & \text { List I } & \text { List II } \\ \hline \text { (A) } & \text { Focus } & \text { (I) }(4,2) \\ \hline \text { (B) } & \text { Vertex } & \text { (II) }(3,2) \\ \hline \text { (C) } & \begin{array}{l} \text { One end of the } \\ \text { latusrectum } \end{array} & \text { (III) }(2,3) \\ \hline \text { (D) } & \begin{array}{l} \text { point of intersection of the } \\ \text { axis and directrix } \end{array} & \text { (IV) }(2,4) \\ \hline & & \text { (V) }(2,2) \\ \hline \end{array} $$

$$ \text { The correct match is } $$