A particular case of quadratic transformation is the

Here we show that the isotomic transformation of ABC coincides with the quadratic transformation of a special family of conics consisting entirely of hyperbolas. The family namely consists of all conics passing through the four points {G,A',B',C'}, where G is the centroid and {A',B',C'} are the vertices of the antiparallel triangle of ABC (created by parallels to the sides from the opposite vertices). All these conics are hyperbolas. Their family is generated by the linear combinations of two degenerate members c

The proof, modulo the remarks made above, is trivial. Apply the definition of the quadratic transformation by taking the polars of P with respect to c

Although the property has a simple proof. The context involves several interesting ideas studied in the references given below.

Quadratic_Transformation.html

Quadratic_Transformation2.html

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