The diagram shows the curve with equation \(y = 4x^{\frac{1}{2}}\).

(i) The straight line with equation \(y = x + 3\) intersects the curve at points \(A\) and \(B\). Find the length of \(AB\).

(ii) The tangent to the curve at a point \(T\) is parallel to \(AB\). Find the coordinates of \(T\).

(iii) Find the coordinates of the point of intersection of the normal to the curve at \(T\) with the line \(AB\).