7. A curve has parametric equations
$$x = t ( t - 1 ) , \quad y = \frac { 4 t } { 1 - t } , \quad t \neq 1$$
- Find \(\frac { \mathrm { d } y } { \mathrm {~d} x }\) in terms of \(t\).
The point \(P\) on the curve has parameter \(t = - 1\).
- Show that the tangent to the curve at \(P\) has the equation
$$x + 3 y + 4 = 0$$
The tangent to the curve at \(P\) meets the curve again at the point \(Q\).
- Find the coordinates of \(Q\).
7. continued