Chapter 8.2, Problem 64SE

For the following exercises, a hedge is to be constructed in the shape of a hyperbola near a fountain at the center of the yard. Find the equation of the hyperbola and sketch the graph.

64. The hedge will follow the asymptotes $y=\frac{2}{3}x$ and $y=-\frac{2}{3}x$ , and its closest distance to the center fountain is 12 yards.