- The curve \(C\) has parametric equations
$$x = t ^ { 2 } + 6 t - 16 \quad y = 6 \ln ( t + 3 ) \quad t > - 3$$
- Show that a Cartesian equation for \(C\) is
$$y = A \ln ( x + B ) \quad x > - B$$
where \(A\) and \(B\) are integers to be found.
The curve \(C\) cuts the \(y\)-axis at the point \(P\)
- Show that the equation of the tangent to \(C\) at \(P\) can be written in the form
$$a x + b y = c \ln 5$$
where \(a\), \(b\) and \(c\) are integers to be found.