10. A curve has the equation \(y = x + \frac { 3 } { x } , x \neq 0\).
The point \(P\) on the curve has \(x\)-coordinate 1 .
- Show that the gradient of the curve at \(P\) is - 2 .
- Find an equation for the normal to the curve at \(P\), giving your answer in the form \(y = m x + c\).
- Find the coordinates of the point where the normal to the curve at \(P\) intersects the curve again.