(i) At \(x = 2\), the gradient \(m = k - 4\). At \(x = 3\), the gradient \(m = k - 6\). Since the tangents are perpendicular, \((k - 4)(k - 6) = -1\).

Solving \((k - 4)(k - 6) = -1\):

\(k^2 - 10k + 24 = -1\)

\(k^2 - 10k + 25 = 0\)

\((k - 5)^2 = 0\)

\(k = 5\)

(ii) Integrate \(\frac{dy}{dx} = 5 - 2x\) to find \(y\):

\(y = 5x - x^2 + c\)

Substitute the point (4, 9):

\(9 = 5(4) - 4^2 + c\)

\(9 = 20 - 16 + c\)

\(c = 5\)

Thus, the equation of the curve is \(y = 5x - x^2\).