6 A surface \(S\) has equation \(z = \mathrm { f } ( x , y )\), where \(\mathrm { f } ( x , y ) = 2 x ^ { 2 } - y ^ { 2 } + 3 x y + 17 y\). It is given that \(S\) has a single stationary point, \(P\).

1. Determine the coordinates, and the nature, of \(P\).
2. Find the equation of the tangent plane to \(S\) at the point \(Q ( 1,2,38 )\).