10. Given that point $P$ lies on the hyperbola $\frac{x^{2}}{16}-\frac{y^{2}}{9}=1$, and the distance from $P$ to the right directrix of this hyperbola is exactly the arithmetic mean of the distances from $P$ to the two foci of this hyperbola. Then, the x-coordinate of $P$ is $\qquad$ .
If $x_{P}0$, then $x_{P}-\frac{a^{2}}{c}=e x_{P} \Rightarrow x_{P}-\frac{16}{5}=\frac{5}{4} x_{P} \Rightarrow x_{P}=-\frac{64}{5}$, contradiction. Therefore, the x-coordinate of point $P$ is $-\frac{64}{5}$.