A curve satisfies $\frac{dy}{dx} = \frac{2}{\sqrt{x}} - 1$ and $P(9, 5)$ lies on the curve.
(i)[4]
Find the equation of the curve.
(ii)[3]
Find the coordinates of the stationary point on the curve.
(iii)[2]
Find an expression for $\frac{d^2 y}{dx^2}$ and determine the nature of the stationary point.
(iv)[2]
The normal to the curve at $P$ makes an angle of $\tan^{-1} k$ with the positive $x$-axis. Find the value of $k$.
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