### Basic Examples (2)

Define a hyperbolic paraboloid:

The focal sets of the hyperbolic paraboloid are given by:

Plot an hyperbolic paraboloid (yellow) and its focal sets (blue and green):

Define an elliptic paraboloid:

The focal sets of an elliptic paraboloid are given by:

Plot an elliptic paraboloid (yellow) and its focal sets (blue and green):

### Scope (4)

A circular helicoid:

Here are the two focal sets of the helicoid:

Plot the focal sets:

Compute the focal sets of a monkey saddle:

Plot of the focal sets of the monkey saddle:

It will be shown in the next example that one of the focal sets of a surface of revolution generated by a plane curve *c* is the surface of revolution generated by the evolute of *c*. First define a tractrix:

Here is its evolute, as returned by the resource function EvoluteCurve:

The evolute of a tractrix is a catenary:

Define a catenoid, i.e. the surface of revolution of a catenary:

Define a surface of revolution:

Compute its focal set for the first curvature:

Plot the pseudosphere and the catenoid (the surface of revolution of a catenary) focal sets:

Define an elliptic‐hyperbolic cyclide:

Compute its focal sets:

Define a function to generate a cyclide together with its focal curves:

The ring cyclide with its focal curves:

The horn cyclide with its focal curves:

The spindle cyclide with its focal curves: