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geometry

  

Polar

  

find the polar of a given point with respect to a given conic or a given circle

 

Calling Sequence

Parameters

Description

Examples

Calling Sequence

Polar(l, P, c)

Parameters

l

-

the name of the polar

A

-

point

e

-

conic or circle

Description

• 

Let c=Or be a fixed circle, and let P be any ordinary point other than O. Let P' be the inverse of P in circle c. Then the line p through P' and perpendicular to OPP' is called the polar of P for the circle c. Since the package does not work with the extended plane, the routine does not find the polar of center O or of the ideal point.

• 

If the point lies on the conic then the polar of P is the tangent line of the conic at that point.

• 

For a detailed description of the polar of P, use the routine detail

• 

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

Examples

withgeometry:

circlec,x2+y2=1,x,y,ellipsee,x24+y2=1,x,y:

pointA,3,0:

Polarl1,A,c

l1

(1)

Equationl1

1+3x=0

(2)

Polarl2,A,e

l2

(3)

detaill2

name of the objectl2form of the objectline2dequation of the line1+3x4=0

(4)

See Also

geometry[inversion]

geometry[Pole]

 


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