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conic

  

define a conic

 

Calling Sequence

Parameters

Description

Examples

Calling Sequence

conic(p, [A, B, C, E, F], n)

conic(p, [dir, fou, ecc], n)

conic(p, eqn, n)

Parameters

p

-

the name of the conic

A, B, C, E, F

-

five distinct points

dir

-

the line which is the directrix of the conic

fou

-

point which is the focus of the conic

ecc

-

a positive number denoting the eccentricity of the conic

eqn

-

the algebraic representation of the conic (i.e., a polynomial or an equation)

n

-

(optional) list of two names representing the names of the horizontal-axis and vertical-axis

Description

• 

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.

Examples

withgeometry:

define conic c1 from its algebraic representation:

_EnvHorizontalName'x':_EnvVerticalName'y':

conicc1,x22xy+y26x10y+9=0,x,y:

formc1

parabola2d

(1)

detailc1

name of the objectc1form of the objectparabola2dvertex0,1focus1,2directrix2x2+2y2+22=0equation of the parabolax22xy+y26x10y+9=0

(2)

linel,x=2,x,y:pointf,1,0:e12:

conicc2,l,f,e,c,d:

formc2

ellipse2d

(3)

pointA,1,2103,pointB,2,2133,pointC,3,22,pointE,4,103,pointF,5,2343:

conicc3,A,B,C,E,F,t1,t2:

formc3

hyperbola2d

(4)

conicc4,x26x+13+y24y9,x,y:

ellipse:   "the given equation is indeed a circle"

formc4

circle2d

(5)

conicc5,x2+y24x10y+29=0,x,y:

conic:   "degenerate case: single point"

degenerate case of an ellipse

detailc5

name of the objectc5form of the objectpoint2dcoordinates of the point2,5

(6)

conicc6,x22xy+2x+y22y+1,x,y:

conic:   "degenerate case: a double line"

degenerate case of a parabola

detailc6

name of the objectc6form of the objectline2dequation of the line2x2+2y2=0

(7)

conicc7,x22xy4x+y2+4y77,x,y

conic:   "degenerate case: two ParallelLine lines"

Line_1_c7,Line_2_c7

(8)

degenerate case of a parabola

detailc7

name of the objectLine_1_c7form of the objectline2dequation of the line2x2+2y2+1122=0,name of the objectLine_2_c7form of the objectline2dequation of the line2x2+2y2722=0

(9)

conicc8,11x2+24xy+4y2+26x+32y+15=0,x,y

conic:   "degenerate case: two intersecting lines"

Line_1_c8,Line_2_c8

(10)

the degenerate case of a hyperbola

detailc8

name of the objectLine_1_c8form of the objectline2dequation of the linex+2y+1=0,name of the objectLine_2_c8form of the objectline2dequation of the line11x52y53=0

(11)

See Also

geometry[draw]

geometry[HorizontalName]

geometry[objects]

geometry[VerticalName]

 


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