Let the focal chord of the parabola $P : y ^ { 2 } = 4 x$ along the line $L : y = m x + c , m > 0$ meet the parabola at the points $M$ and $N$. Let the line $L$ be a tangent to the hyperbola $H : x ^ { 2 } - y ^ { 2 } = 4$. If $O$ is the vertex of $P$ and $F$ is the focus of $H$ on the positive $x$-axis, then the area of the quadrilateral $O M F N$ is\\
(1) $2 \sqrt { 6 }$\\
(2) $2 \sqrt { 14 }$\\
(3) $4 \sqrt { 6 }$\\
(4) $4 \sqrt { 14 }$