8. The hyperbola \(H\) has cartesian equation \(x y = 16\)
The parabola \(P\) has parametric equations \(x = 8 t ^ { 2 } , y = 16 t\).
- Find, using algebra, the coordinates of the point \(A\) where \(H\) meets \(P\).
Another point \(B ( 8,2 )\) lies on the hyperbola \(H\).
- Find the equation of the normal to \(H\) at the point (8, 2), giving your answer in the form \(y = m x + c\), where \(m\) and \(c\) are constants.
- Find the coordinates of the points where this normal at \(B\) meets the parabola \(P\).