Chapter 13.3, Problem 49ES

In Exercises 47-50, determine whether each statement is true or false. If the Statement is false, make the necessary change(s) to produce a true statement.

47. If one branch of a hyperbola is removed from a graph, then the branch that remains must define y as a function of x.

48. All points on the asymptotes of a hyperbola also satisfy the hyperbola’s equation.

49. The graph of $\frac{x^2}{9}-\frac{y^2}{4}=1$ does not intersect the line $y=-\frac{2}{3}x$ .

50. Two different hyperbolas can never share the same asymptotes.