8. The rectangular hyperbola \(H\) has equation \(x y = c ^ { 2 }\).
The point ( \(3 t , \frac { 3 } { t }\) ) is a general point on this hyperbola.
- Find the value of \(c ^ { 2 }\).
- Show that an equation of the normal to \(H\) at the point ( \(3 t , \frac { 3 } { t }\) ) is
$$y = t ^ { 2 } x + \left( \frac { 3 } { t } - 3 t ^ { 3 } \right)$$
The point \(P\) on \(H\) has coordinates (6, 1.5). The tangent to \(H\) at \(P\) meets the curve again at the point \(Q\).
- Find the coordinates of the point \(Q\).