Shape

Multivariable functions sometimes produce shapes of particular names.

Index of common shapes

Ellipsoid, with equation $\frac{x^2}{a^2}+\frac{y^2}{b^2}+\frac{z^2}{c^2}=d,d\in \mathbb{R}$. All traces are ellipses. Elliptic paraboloid, with equation $z=\frac{x^2}{a^2}+\frac{y^2}{b^2}$