A conic 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 conic.

from the directrix, focus, and eccentricity. The input is a list of the form [dir, fou, ecc] where dir, fou, and ecc 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.

The routine returns a conic which includes the degenerate cases for the given input. The output is one of the following object: (or list of objects)

a parabola

an ellipse

a hyperbola

a circle

a point (ellipse: degenerate case)

two parallel lines or a "double" line (parabola: degenerate case)

a list of two intersecting lines (hyperbola: degenerate case)

The information relating to the output conic p depends on the type of output. Use the routine geometry[form] to check for the type of output. For a detailed description of the conic p, use the routine detail (i.e., detail(p))

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

ellipse:   "the given equation is indeed a circle"

conic:   "degenerate case: single point"

conic:   "degenerate case: a double line"

conic:   "degenerate case: two ParallelLine lines"

conic:   "degenerate case: two intersecting lines"