- A rectangular hyperbola \(H\) has equation \(x y = 25\)
The point \(P \left( 5 t , \frac { 5 } { t } \right) , t \neq 0\), is a general point on \(H\).
- Show that the equation of the tangent to \(H\) at \(P\) is \(t ^ { 2 } y + x = 10 t\)
The distinct points \(Q\) and \(R\) lie on \(H\). The tangent to \(H\) at the point \(Q\) and the tangent to \(H\) at the point \(R\) meet at the point \(( 15 , - 5 )\).
- Find the coordinates of the points \(Q\) and \(R\).