8 The equation of a curve is \(x ^ { 3 } + y ^ { 3 } = 6 x y\).
- Find \(\frac { \mathrm { d } y } { \mathrm {~d} x }\) in terms of \(x\) and \(y\).
- Show that the point \(\left( 2 ^ { \frac { 4 } { 3 } } , 2 ^ { \frac { 5 } { 3 } } \right)\) lies on the curve and that \(\frac { \mathrm { d } y } { \mathrm {~d} x } = 0\) at this point.
- The point \(( a , a )\), where \(a > 0\), lies on the curve. Find the value of \(a\) and the gradient of the curve at this point.