10. A curve has the equation \(y = ( \sqrt { x } - 3 ) ^ { 2 } , x \geq 0\).
- Show that \(\frac { \mathrm { d } y } { \mathrm {~d} x } = 1 - \frac { 3 } { \sqrt { x } }\).
The point \(P\) on the curve has \(x\)-coordinate 4 .
- Find an equation for the normal to the curve at \(P\) in the form \(y = m x + c\).
- Show that the normal to the curve at \(P\) does not intersect the curve again.