Let $H$ : $\frac { x ^ { 2 } } { a ^ { 2 } } - \frac { y ^ { 2 } } { b ^ { 2 } } = 1$, where $a > b > 0$, be a hyperbola in the $x y$-plane whose conjugate axis $L M$ subtends an angle of $60 ^ { \circ }$ at one of its vertices $N$. Let the area of the triangle $L M N$ be $4 \sqrt { 3 }$.

\textbf{LIST-I}\\
P. The length of the conjugate axis of $H$ is\\
Q. The eccentricity of $H$ is\\
R. The distance between the foci of $H$ is\\
S. The length of the latus rectum of $H$ is

\textbf{LIST-II}
\begin{enumerate}
  \item 8
  \item $\frac { 4 } { \sqrt { 3 } }$
  \item $\frac { 2 } { \sqrt { 3 } }$
  \item 4
\end{enumerate}

The correct option is:\\
(A) $\mathbf { P } \rightarrow \mathbf { 4 } ; \mathbf { Q } \rightarrow \mathbf { 2 } ; \mathbf { R } \rightarrow \mathbf { 1 } ; \mathbf { S } \rightarrow \mathbf { 3 }$\\
(B) $\mathbf { P } \rightarrow \mathbf { 4 } ; \mathbf { Q } \rightarrow \mathbf { 3 } ; \mathbf { R } \rightarrow \mathbf { 1 } ; \mathbf { S } \rightarrow \mathbf { 2 }$\\
(C) $\mathbf { P } \rightarrow \mathbf { 4 } ; \mathbf { Q } \rightarrow \mathbf { 1 } ; \mathbf { R } \rightarrow \mathbf { 3 } ; \mathbf { S } \rightarrow \mathbf { 2 }$\\
(D) $\mathbf { P } \rightarrow \mathbf { 3 } ; \mathbf { Q } \rightarrow \mathbf { 4 } ; \mathbf { R } \rightarrow \mathbf { 2 } ; \mathbf { S } \rightarrow \mathbf { 1 }$