2024 VJC H1 Q3

The curve \(C\) has equation \(y = \ln(k - 2x)\) where \(k\) is a negative constant. Sketch the graph of \(C\), stating, in terms of \(k\), the coordinates of any point(s) of intersection with the axes and the equation of any asymptote(s).[2]

It is given now that \(k = -3\). The equation of the tangent to \(C\) at \(x = -\frac{5}{2}\) cuts the \(x\)-axis and the \(y\)-axis at point \(P\) and point \(Q\) respectively. Find the exact area of the triangle \(OPQ\).[4]