find the reciprocation of a point or a line with respect to a circle
reciprocation(Q, P, c)
the name of the object to be created
point or line
Let c=O⁡r be a fixed circle and let P be any ordinary point other than the center O. Let P' be the inverse of P in circle O⁡r. Then the line Q through P' and perpendicular to OPP' is called the polar of P for the circle c. Note that when P is a line, then Q will be a point.
Note that this routine in particular, and the geometry package in general, does not encompass the extended plane, i.e., the polar of center O does not exist (though in the extended plane, it is the line at infinity) and the polar of an ideal point P does not exist either (it is the line through the center O perpendicular to the direction OP in the extended plane).
If line Q is the polar point P, then point P is called the pole of line Q.
The pole-polar transformation set up by circle c=O⁡r is called reciprocation in circle c
For a detailed description of Q (the object created), use the routine detail (i.e., detail(Q))
The command with(geometry,reciprocation) allows the use of the abbreviated form of this command.
name of the objectlform of the objectline2dequation of the line−4+x=0
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