This completely defines projectivity f with the properties:

- It maps line [AD] to [BC] by acting as parallel translation (parallel to AB) at every point of line [AD].

- It maps line [BC] to [AD] acting by the symmetry at O at every point of line [BC].

- It maps the ellipse inscribed in the rectangle:

An easy calculation, using the recipe given in Projectivity.html , shows that the matrix describing the transformation (f) is:

HyperbolaGeneration2.html

Projectivity.html

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