Answer
See graph
Work Step by Step
$$4x^2-y^2=36$$
$$\frac{x^2}{9}-\frac{y^2}{36}=1$$
The center of the hyperbola is (0,0). The four corners of the box are (3,6), (-3,6), (3,-6) and (-3,-6). Draw a dotted box through these points. Then draw two dotted lines through the corners. The vertices of the hyperbola are (3,0) and (-3,0), so plot those points and draw a smooth curve nearing the two asymptotes without touching them.
