Calc 3 Equations

$$x^2 + y^2 = 4$$

Cylinder

$$\frac{x^2}{4} + \frac{y^2}{9} + \frac{z^2}{16} = 1$$

Ellipsoid

$$\frac{x^2}{4} + \frac{y^2}{9} = z$$

Elliptic Paraboloid

$$\frac{x^2}{4} - \frac{y^2}{9} = z$$

Hyperbolic Paraboloid

$$\frac{x^2}{4} + \frac{y^2}{9} - \frac{z^2}{16} = 1$$

Hyperboloid of 1 Sheet

$$\frac{x^2}{4} - \frac{y^2}{9} - \frac{z^2}{16} = 1$$

Hyperboloid of 2 Sheets

$$\frac{x^2}{4} + \frac{y^2}{9} - \frac{z^2}{16} = 0$$

Stacked Cones

Cylinder

An equation in two variables (missing one coordinate variable) where the trace in the coordinate plane parallel to the missing axis is repeated along that axis

Ellipsoid

An equation where all variables are squared

Elliptic Paraboloid

An equation with two squared variables having positive coefficients equal to a linear (first-power) variable

Hyperbolic Paraboloid

An equation with two squared variables of opposite signs equal to a linear variable

Hyperboloid of 1 Sheet

An equation where all three variables are squared

Hyperboloid of 2 Sheets

An equation where all three variables are squared

Stacked Cones (Elliptic Cone)

An equation where all three variables are squared