(x-a)*(y-b) = a*b,

satisfied by the parameters x, y of two points X, Y intersected on two lines e

through a fixed point P.

The map Y=f(X) of line e

See the discussion in ProjectiveLine.html for the theoretical background.

This is a particular example of a wide class of maps between the points of two lines, called

The basics for such relations are discussed in the file ProjectiveLine.html and HomographicRelation.html . Points X

and Y=f(X) are supposed to be defined by X = (1-x)*A+x*B and E = (1-y)*A+y*C. The hyperbola depends on the

four points A, B, C and P. It is constructed in two stages (through user-defined tools of EucliDraw).

Rectangular hyperbolas are discussed in the references below.

Maclaurin's theorem ( Maclaurin.html ) and Chasles-Steiner theorem ( Chasles_Steiner.html ).

HomographicRelation.html

Maclaurin.html

Chasles_Steiner.html

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