- The rectangular hyperbola \(H\) has Cartesian equation \(x y = 9\)
The point \(P\) with coordinates \(\left( 3 t , \frac { 3 } { t } \right)\), where \(t \neq 0\), lies on \(H\)
- Use calculus to determine an equation for the normal to \(H\) at the point \(P\)
Give your answer in the form \(t y - t ^ { 3 } x = \mathrm { f } ( t )\)
Given that \(t = 2\)
- determine the coordinates of the point where the normal meets \(H\) again.
Give your answer in simplest form.