8. A curve has parametric equations
$$x = t ^ { 2 } - t , \quad y = \frac { 4 t } { 1 - t } \quad t \neq 1$$
- Find \(\frac { \mathrm { d } y } { \mathrm {~d} x }\) in terms of \(t\), giving your answer as a simplified fraction.
- Find an equation for the tangent to the curve at the point \(P\) where \(t = - 1\), giving your answer in the form \(a x + b y + c = 0\) where \(a , b\) and \(c\) are integers.
The tangent to the curve at \(P\) cuts the curve at the point \(Q\).
- Use algebra to find the coordinates of \(Q\).