1 The surface \(E\) has equation \(z = \sqrt { 500 - 3 x ^ { 2 } - 2 y ^ { 2 } }\).
- Determine the values of \(\frac { \partial z } { \partial x }\) and \(\frac { \partial z } { \partial y }\) at the point \(P\) on \(E\) with coordinates \(( 11 , - 8,3 )\).
- Find the equation of the tangent plane to \(E\) at \(P\), giving your answer in the form \(\mathrm { ax } + \mathrm { by } + \mathrm { cz } = \mathrm { d }\) where \(a , b , c\) and \(d\) are integers.