Question 126
Suppose that the line $l$: $y = kx + m$ ($k$, $m$ are integers) intercepts an ellipse $\frac{x^2}{16} + \frac{y^2}{12} = 1$ at two different points $A$, $B$, and intercepts the hyperbola $\frac{x^2}{4} - \frac{y^2}{12} = 1$ at two different points $C$, $D$. Can the line $l$ be such that $\vec{AC} + \vec{BD} = 0$? If yes, how many different possibilities are there for the line $l$? If no, explain the reason.