Let T and C respectively, be the transverse and conjugate axes of the hyperbola $16 x ^ { 2 } - y ^ { 2 } + 64 x + 4 y + 44 = 0$. Then the area of the region above the parabola $x ^ { 2 } = y + 4$, below the transverse axis T and on the right of the conjugate axis C is:\\
(1) $4 \sqrt { 6 } + \frac { 44 } { 3 }$\\
(2) $4 \sqrt { 6 } + \frac { 28 } { 3 }$\\
(3) $4 \sqrt { 6 } - \frac { 44 } { 3 }$\\
(4) $4 \sqrt { 6 } - \frac { 28 } { 3 }$