1.5.3 Circles
Refresh your memory on the standard way to parameterize a circle in the plane.
This can be rewritten this way:
In we can shift our circle out of the plane by finding two non-zero orthogonal vectors in the plane containing our circle. If is the center of the circle and and are two orthogonal vectors in the plane containing our circle, then we have the following parameterization:
The GeoGebra file below illustrates this approach. Have a conversation with a partner about why this works. Why are we dividing by and ? What happens if and are not orthogonal?