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\includegraphics[max width=\textwidth, alt={}, center]{518bb805-5b14-4b41-94fd-38a31a90c218-18_551_689_260_726}
The diagram shows part of the curve \(y = \sqrt { } ( 5 x - 1 )\) and the normal to the curve at the point \(P ( 2,3 )\). This normal meets the \(x\)-axis at \(Q\).
- Find the equation of the normal at \(P\).
- Find, showing all necessary working, the area of the shaded region.