Match the following lists:
\begin{tabular}{|l|l|c|c|}
\hline \multicolumn{1}{|c|}{ List-I } & \multicolumn{2}{|l|}{ List-II } \\
\hline A. & \begin{tabular}{l}
If \( \mathrm{z} \) is a complex number such \\
that \( \operatorname{Im}\left(\mathrm{z}^{2}\right)=3 \), then the \\
eccentricity of the locus is
\end{tabular} & P. & \\
\hline B. & \begin{tabular}{l}
If the latus rectum of a \\
hyperbola through one focus \\
subtends an angle of \( 60^{\circ} \) at the \\
other focus, then its eccentricity \\
is
\end{tabular} & Q. & \\
\hline C. & \begin{tabular}{l}
If \( \mathrm{A} \equiv(3,0) \) and \( \mathrm{B} \equiv(-3,0) \) and \\
PA-PB \( =4 \) the eccentricity of \\
conjugate hyperbola is
\end{tabular} & R. & \( \sqrt{2} \) \\
\hline D. & \begin{tabular}{l}
If the angle between the \\
asymptotes of a hyperbola is \( \frac{\pi}{3} \), \\
then the eccentricity of its \\
conjugate hyperbola is
\end{tabular} & \( \mathrm{S} \) & \( \frac{3}{\sqrt{5}} \) \\
\hline
\end{tabular}
\( \mathrm{P} \)
W
A
B
(1) \( \mathrm{Q} \)
(2) \( \mathrm{R} \)
(3) \( \mathrm{P} \)
(4) \( \mathrm{P} \)
P
D
\( P \)
Q
C
S
Q
\( \begin{array}{ll}\mathrm{S} & \mathrm{Q} \\ \mathrm{S} & \mathrm{R}\end{array} \)
R
Q
\( \mathrm{S} \)
0