- The curve \(C\) has equation
$$y = 9 - 4 x - \frac { 8 } { x } , \quad x > 0$$
The point \(P\) on \(C\) has \(x\)-coordinate equal to 2 .
- Show that the equation of the tangent to \(C\) at the point \(P\) is \(y = 1 - 2 x\).
- Find an equation of the normal to \(C\) at the point \(P\).
The tangent at \(P\) meets the \(x\)-axis at \(A\) and the normal at \(P\) meets the \(x\)-axis at \(B\).
- Find the area of triangle \(A P B\).