- The curve \(C\) has parametric equations
$$x = 3 t - 4 , y = 5 - \frac { 6 } { t } , \quad t > 0$$
- Find \(\frac { \mathrm { d } y } { \mathrm {~d} x }\) in terms of \(t\)
The point \(P\) lies on \(C\) where \(t = \frac { 1 } { 2 }\)
- Find the equation of the tangent to \(C\) at the point \(P\). Give your answer in the form \(y = p x + q\), where \(p\) and \(q\) are integers to be determined.
- Show that the cartesian equation for \(C\) can be written in the form
$$y = \frac { a x + b } { x + 4 } , \quad x > - 4$$
where \(a\) and \(b\) are integers to be determined.