2026 GESS P2 Q8

The diagram shows part of the curve \(y=\dfrac3{2x-1}+\dfrac13x\) where \(x\ne\dfrac12\) and the line \(x=4\). The normal to the curve at the point \(P(a,b)\) cuts the \(x\)-axis at \(A\).

Given that the gradient of this normal is \(\dfrac67\), calculate

1. the value of \(a\) and of \(b\),[5]
2. the area of the shaded region.[5]