5 A surface \(S\) is defined for \(z \geqslant 0\) by \(x ^ { 2 } + y ^ { 2 } + 2 z ^ { 2 } = 126\). \(C\) is the set of points on \(S\) for which the tangent plane to \(S\) at that point intersects the \(x - y\) plane at an angle of \(\frac { 1 } { 3 } \pi\) radians. Show that \(C\) lies in a plane, \(\Pi\), whose equation should be determined.