2025 PHS PRELIMS P1 Q13

The diagram shows part of the curve \(y = \sqrt{2x + 5}\). \(A\) is a point on the curve and the \(x\)-coordinate of \(A\) is \(2\). The normal to the curve at \(A\) meets the \(x\)-axis at \(B\).

1. Find the equation of the normal to the curve at \(A\).[5]
2. Find the area of the shaded region bounded by the normal \(AB\), the curve, the \(x\)-axis and the \(y\)-axis.[5]