define a conic
conic(p, [A, B, C, E, F], n)
conic(p, [dir, fou, ecc], n)
conic(p, eqn, n)
the name of the conic
A, B, C, E, F
five distinct points
the line which is the directrix of the conic
point which is the focus of the conic
a positive number denoting the eccentricity of the conic
the algebraic representation of the conic (i.e., a polynomial or an equation)
(optional) list of two names representing the names of the horizontal-axis and vertical-axis
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 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.
define conic c1 from its algebraic representation:
_EnvHorizontalName ≔ 'x':_EnvVerticalName ≔ 'y':
name of the objectc1form of the objectparabola2dvertex0,1focus1,2directrix2⁢x2+2⁢y2+22=0equation of the parabolax2−2⁢x⁢y+y2−6⁢x−10⁢y+9=0
line⁡l,x=−2,x,y:point⁡f,1,0:e ≔ 12:
ellipse: "the given equation is indeed a circle"
conic: "degenerate case: single point"
degenerate case of an ellipse
name of the objectc5form of the objectpoint2dcoordinates of the point2,5
conic: "degenerate case: a double line"
degenerate case of a parabola
name of the objectc6form of the objectline2dequation of the line−2⁢x2+2⁢y2=0
conic: "degenerate case: two ParallelLine lines"
name of the objectLine_1_c7form of the objectline2dequation of the line−2⁢x2+2⁢y2+11⁢22=0,name of the objectLine_2_c7form of the objectline2dequation of the line−2⁢x2+2⁢y2−7⁢22=0
conic: "degenerate case: two intersecting lines"
the degenerate case of a hyperbola
name of the objectLine_1_c8form of the objectline2dequation of the linex+2⁢y+1=0,name of the objectLine_2_c8form of the objectline2dequation of the line−11⁢x5−2⁢y5−3=0
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