10 A curve is such that \(\frac { \mathrm { d } y } { \mathrm {~d} x } = \frac { 2 } { a } x ^ { - \frac { 1 } { 2 } } + a x ^ { - \frac { 3 } { 2 } }\), where \(a\) is a positive constant. The point \(A \left( a ^ { 2 } , 3 \right)\) lies on the curve. Find, in terms of \(a\),
- the equation of the tangent to the curve at \(A\), simplifying your answer,
- the equation of the curve.
It is now given that \(B ( 16,8 )\) also lies on the curve.
- Find the value of \(a\) and, using this value, find the distance \(A B\).