Circles and Parabolas in 3-Space

This edition's column had its genesis with a question and a discovery

The question: How do you find the equations for circles and parabolas in 3-space?

The discovery: GeoGebra 5, the latest GeoGebra update, now has a 3D component (Figure 1) that allows you to define and plot curves and surfaces parametrically using the command Curve[ Expression, Expression, Expression, Parameter Variable, Start Value, End Value ].
Curves can also be defined constructively using a variety of tools that appear in the MENU bar. There is an Input Window where one can enter points, vectors, and implicit definitions of surfaces such as planes. Any time a curve is defined either by entry or by construction, relevant information about it appears in the Algebra Window.