The graphs of f(x) = a(x+p)² + q and g(x) = -8/(x-1) + 9 are drawn below. P is the turning point of f and the point of intersection of the asymptotes of g. The graphs intersect at D(3; 5) M and T are the x-intercepts of f and g respectively. A and B are the y-intercepts of f and g respectively.

The function $g(x)$ is given by $g(x) = \frac{-8}{x-1} + 9$.
For a hyperbola in the form $y = \frac{a}{x-p} + q$, the vertical asymptote is $x=p$ and the horizontal asymptote is $y=q$.

From $g(x) = \frac{-8}{x-1} + 9$, we have:
Vertical asymptote: $x = 1$
Horizontal asymptote: $y = 9$

P is the point of intersection of the asymptotes of $g$. Therefore, the coordinates of P are the values of $x$ and $y$ from the asymptotes.
$P = (1, 9)$

The coordinates of P are $\boxed{(1; 9)}$.