Mathematics

The asymptotes of a hyperbola reveal the "ultimate direction" the curve heads toward as you move far from the center. For a hyperbola in standard form $\frac{x^2}{a^2} - \frac{y^2}{b^2} = 1$, the asymptotes come from setting the equation equal to zero instead of 1—this gives you the pair of lines the hyperbola approaches. The slopes are simply $\pm\frac{b}{a}$, the ratio of the vertical and horizontal scale factors.

The asymptotes of a hyperbola reveal the "ultimate direction" the curve heads toward as you move far from the center. For a hyperbola in standard form $\frac{x^2}{a^2} - \frac{y^2}{b^2} = 1$, the asymptotes come from setting the equation equal to zero instead of 1—this gives you the pair of lines the hyperbola approaches. The slopes are simply $\pm\frac{b}{a}$, the ratio of the vertical and horizontal scale factors.