8 A curve has parametric equations
$$x = \frac { 1 } { t + 1 } , \quad y = t - 1 .$$
The line \(y = 3 x\) intersects the curve at two points.
- Show that the value of \(t\) at one of these points is - 2 and find the value of \(t\) at the other point.
- Find the equation of the normal to the curve at the point for which \(t = - 2\).
- Find the value of \(t\) at the point where this normal meets the curve again.
- Find a cartesian equation of the curve, giving your answer in the form \(y = \mathrm { f } ( x )\).