9. Given two points $M(-5,0)$ and $N(5,0)$. If there exists a point $P$ on a line such that $|P M|-|P N|=6$, then the line is called a "harmonious line". Given the following lines:
(1) $y=x-1$;
(2) $y=2$;
(3) $y=\frac{5}{3} x$;
(4) $y=2 x+1$,

which of these lines are harmonious lines? $\qquad$
9. (1),(2).

This problem is transformed into finding the intersection of a line with the right branch of the hyperbola $\frac{x^{2}}{9}-\frac{y^{2}}{16}=1$. By analyzing the positional relationship between the lines in the options and the asymptote $y=\frac{4}{3} x$ of the hyperbola, it is easy to see that (1) and (2) are correct.