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\includegraphics[max width=\textwidth, alt={}, center]{a10ad459-6f86-4845-ba28-e4e394bf3d1e-4_595_800_1548_669}
The diagram shows the points \(A ( 1,2 )\) and \(B ( 4,4 )\) on the curve \(y = 2 \sqrt { } x\). The line \(B C\) is the normal to the curve at \(B\), and \(C\) lies on the \(x\)-axis. Lines \(A D\) and \(B E\) are perpendicular to the \(x\)-axis.
- Find the equation of the normal \(B C\).
- Find the area of the shaded region.