A curve \(C\) is defined by the parametric equations
Find the coordinates of the point on \(C\) where the tangent is parallel to the \(x\)-axis.[3]
Sketch \(C\). (You do not need to give the coordinates of the axial intercepts)[1]
The line \(N\) is the normal to \(C\) at the point where \(t=2\). Show that the equation of \(N\) is \(3y-x=29\).[2]
Without the use of a graphing calculator, show that the line \(N\) does not meet the curve \(C\) again.[4]