8. In a rectangular coordinate system, given two points $A(0, a), B(0, b), a>b>0$ on the positive half of the $y$-axis. $C$ is a point on the positive half of the $x$-axis, and makes $\angle A C B$ maximum, then the coordinates of point $C$ are $\qquad$ .
8. $(\sqrt{a b}, 0)$ Hint: Let $C(x, 0)$, then $k_{A C}=-\frac{a}{x}, k_{B C}=-\frac{b}{x}, \tan \angle A C B=\frac{k_{B C}-k_{A C}}{1+k_{B C} \cdot k_{A C}}=\frac{a-b}{x+\frac{a b}{x}} \leqslant$ $\frac{a-b}{2 \sqrt{a b}}$. (and the equality holds if and only if $x=\sqrt{a b}$)