Symbiotic conics and quartets of four-foci orthogonal circles
The abstract of the paper tells in a condense way, what it is all about. The contents of the paper themselves are technical but informative. The figures in the paper provide a lot of insights, very well alluded to in the text. Here, the following is quoted from the abstract, somewhat shortened: NEWLINE``A quartet of orthogonal circles (one being imaginary) associated with a general \(P\) on a given ellipse \(H\) is described. The mutual intersections of these circles, their intersections with Barlotti's circles and further, newly introduced points are peculiar. As such (Theorem 2.10) one gets a complete, cyclic quadrangle having two diagonal points in fixed positions on the mirror axis of \(H\), these are noncyclic with the foci of \(H\), in spite of the dependence of the whole figure from the point \(P\) location.NEWLINENEWLINE Two conics (the symbolic ellipse \(H_\Sigma\) and the hyperbola \(Y_\Sigma\)) are introduced with respect to \(P\). These conics are characterized by the facts thatNEWLINENEWLINE 1) \(P\) is the center of them and they have the tangent and normal to \(H\) at \(P\) as symmetry axes;NEWLINENEWLINE 2) they pass through the center of \(H\);NEWLINENEWLINE 3) they admit the axes of symmetry of \(H\) as tangent and normal.''NEWLINENEWLINE Besides the impressions presented in the abstract, the paper provides (other) results too, to which the reader is kindly referred to by the reviewer.
scientific article; zbMATH DE number 6627648