9. The rectangular hyperbola \(H\) has cartesian equation \(x y = 9\)
The points \(P \left( 3 p , \frac { 3 } { p } \right)\) and \(Q \left( 3 q , \frac { 3 } { q } \right)\) lie on \(H\), where \(p \neq \pm q\).
- Show that the equation of the tangent at \(P\) is \(x + p ^ { 2 } y = 6 p\).
- Write down the equation of the tangent at \(Q\).
The tangent at the point \(P\) and the tangent at the point \(Q\) intersect at \(R\).
- Find, as single fractions in their simplest form, the coordinates of \(R\) in terms of \(p\) and \(q\).