Common Asymptotes of Conjugate Hyperbolas

Common Asymptotes of Conjugate Hyperbolas

The hyperbola and its conjugate:

$$\frac{x^2}{a^2}-\frac{y^2}{b^2}=1$$

$$\frac{y^2}{b^2}-\frac{x^2}{a^2}=1$$

have the same asymptotes:

$$y=\pm\frac{b}{a}x$$

Usage

- Used to identify conjugate hyperbolas through their common asymptotes.