Consider a cylinder of radius , with axis at a distance from the axis. Its parametric equations are

,

,

,

where and are parameters.

The parametric equation of a sphere with radius is

,

,

,

where and are parameters.

The intersection curve of the two surfaces comes from solving the system of three equations

for three of the four parameters . In this Demonstration, solving for , , and gives the parametric equations for the intersection curve with parameter (the curve consists of four parts, depending on the sign inside the equations for and ).