Chapter 10 - Section 10.2 - The Ellipse and the Hyperbola - Exercise Set - Page 618: 40

See graph

$$\frac{x^2}{16}-\frac{y^2}{4}=1$$ This is a hyperbola with center (0,0). The x-intercepts are (4,0) and (-4,0). The corners of the box are (4,2), (-4,2), (-4,-2), and (4,-2). Draw two asymptotes with dotted lines through the corners. Draw two smooth curves originating at (4,0) and (-4,0) that approach but do not intersect the dotted asymptotes.