Let A be the hyperbola with the equation $\displaystyle \frac{x^2}{a^2} - \frac{y^2}{b^2} = 1$, where $a$ is the $x$-intercept and $b$ is the $y$-intercept.
Given this it can be calculated that the lines $\displaystyle y=\frac{b}{a}\cdot x$ and $\displaystyle y=-\frac{b}{a}\cdot x$ are both asymptotes to the hyperbola.
The question is simply: are these asymptotes significant? And if so, why?