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\includegraphics[max width=\textwidth, alt={}, center]{d0074ac8-42d2-49f4-a417-4a348537bccc-4_521_809_258_669}
The diagram shows part of the curve \(y = ( x - 2 ) ^ { 4 }\) and the point \(A ( 1,1 )\) on the curve. The tangent at \(A\) cuts the \(x\)-axis at \(B\) and the normal at \(A\) cuts the \(y\)-axis at \(C\).
- Find the coordinates of \(B\) and \(C\).
- Find the distance \(A C\), giving your answer in the form \(\frac { \sqrt { } a } { b }\), where \(a\) and \(b\) are integers.
- Find the area of the shaded region.