10. The point \(P \left( 6 t , \frac { 6 } { t } \right) , t \neq 0\), lies on the rectangular hyperbola \(H\) with equation \(x y = 36\).
- Show that an equation for the tangent to \(H\) at \(P\) is
$$y = - \frac { 1 } { t ^ { 2 } } x + \frac { 12 } { t }$$
The tangent to \(H\) at the point \(A\) and the tangent to \(H\) at the point \(B\) meet at the point \(( - 9,12 )\).
- Find the coordinates of \(A\) and \(B\).