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

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

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

$x^2 - y^2 = 1$