Answer:
y = ±(1/3)x
Explanation:
The asymptotes of this hyperbola will contain the diagonals of the green rectangle. The green rectangle at the center of this hyperbola has corners that have a run from its center of 3 for a rise of ±1, so the slope of the line from its center to the corner is rise/run = ±1/3. The center is at (0, 0), so the equations of the asymptotes are
y = ±(1/3)x