2024 FMSS PRELIMS P1 Q11

The diagram shows part of the curve \(y = (9 - x)(x - 3)\) and the line \(y = k - 3\), where \(k > 3\). The line through the maximum point of the curve, parallel to the \(y\)-axis, meets the \(x\)-axis at \(A\). The curve meets the \(x\)-axis at \(B\) and the line \(y = k - 3\) meets the curve at the point \(C(k, k - 3)\).

1. Show that the value of \(k\) is \(8\).[4]
2. Find the area of the shaded region.[5]