A parabola is the set of all points in the plane that are equidistant from a given line and a given point not on the line. A parabola is symmetric about the line that passes through the focus at right angles to the directrix.  This line, called the axis of the parabola, meets the parabola at a point called the vertex.

The given line is called the directrix of the parabola, and the given point the focus.

A parabola p can be defined as follows:

from five distinct points. The input is a list of five points. Note that a set of five distinct points does not necessarily define a parabola.

from the focus and vertex. The input is a list of the form ['focus'=fou, 'vertex'=ver] where fou and ver are explained above.

from the directrix and focus. The input is a list of the form ['directrix'=dir, 'focus'= fou] where dir and fou are explained above.

from its internal representation eqn. The input is an equation or a polynomial. If the optional argument n is not given, then:

if the two environment variables _EnvHorizontalName and _EnvVerticalName are assigned two names, these two names will be used as the names of the horizontal-axis and vertical-axis respectively.

if not, Maple will prompt for input of the names of the axes.

To access the information relating to a parabola p, use the following function calls:

The command with(geometry,parabola) allows the use of the abbreviated form of this command.