Answer
False.
Work Step by Step
False. It is possible that two different hyperbolas have the same asymptotes. For example: $\frac{x^2}{a^2}-\frac{y^2}{b^2}=1$ and $\frac{y^2}{b^2}-\frac{x^2}{a^2}=1$. Another example: $\frac{x^2}{a^2}-\frac{y^2}{b^2}=1$ and $\frac{x^2}{ka^2}-\frac{y^2}{kb^2}=1$
