9. A line with an inclination angle of $\frac{\pi}{4}$ intersects the ellipse $\frac{x^{2}}{4}+y^{2}=1$ at points $A$ and $B$. The equation of the trajectory of the midpoint of segment $A B$ is . $\qquad$
9. $x+4 y=0$, and $|x|<\frac{4}{5} \sqrt{5}$. Hint: You can use the parametric method, set $A(2 \cos \theta, \sin \theta), B(2 \cos \alpha, \sin \alpha)$, then the coordinates of the midpoint of $A B$ are $(x, y)=\left(\cos \theta+\cos \alpha, \frac{\sin \theta+\sin \alpha}{2}\right)$, eliminate the parameters accordingly.