Answer
See graph
Work Step by Step
$$x^2-4y^2=16$$
$$\frac{x^2}{16}-\frac{y^2}{4}=1$$
The center of the hyperbola is (0,0). The four corners of the box are (4,2), (-4,2), (4,-2) and (-4,-2). Draw a dotted box through these points. Then draw two dotted lines through the corners. The vertices of the hyperbola are (4,0) and (-4,0), so plot those points and draw a smooth curve nearing the two asymptotes without touching them.
