$\small \displaystyle z=\frac{x^2}{a^2}+\frac{y^2}{b^2}$
$\small \displaystyle z=\frac{x^2}{a^2}-\frac{y^2}{b^2}$
$\small Ax^2+By^2+Cz^2+Dxy+Exz+Fyz+Gx+Hy+Iz+J=0$