14 The hyperbola \(H\) has equation \(y ^ { 2 } - x ^ { 2 } = 16\) The circle \(C\) has equation \(x ^ { 2 } + y ^ { 2 } = 32\)
The diagram below shows part of the graph of \(H\) and part of the graph of \(C\).
\includegraphics[max width=\textwidth, alt={}, center]{8f7a5fc0-6936-4aed-a173-e221bf86e4fd-22_825_716_539_662} Show that the shaded region in the first quadrant enclosed by \(H , C\), the \(x\)-axis and the \(y\)-axis has area $$\frac { 16 \pi } { 3 } + 8 \ln \left( \frac { \sqrt { 2 } + \sqrt { 6 } } { 2 } \right)$$