9. Find the equations of the $n$ lines passing through the origin and perpendicular to the $n$ lines represented by $a_{0} x^{n}+a_{1} x^{n-1} y+a_{2} x^{n-2} y^{2}+\cdots+a_{n} y^{n}=0$.
9. Let the $n$ lines represented by the original equation be $y=m_{i} x(i=1,2, \cdots, n)$, then their perpendicular lines are $y=-\frac{s 1}{m_{i}} x(i=1$, $2, \cdots, n)$. Therefore, the equation we seek is obtained by replacing $\frac{x}{y}$ with $-\frac{y}{x}$ in the original equation, i.e., $a_{0} y^{n}-a_{1} y^{n-1} x+a_{2} y^{n-2} x^{2}-\cdots+$ $(-1)^{n} u_{n} x^{n}=0$.