An unusual way to generate conic sections. Related Euclidean constructions (Q2778499)

The author gives a constructive approach to conic sections (except for the parabola) as envelopes of families of lines that are generated as follows: Given two points \(A,B\) and a circle \(c\) with center \(X\), take \(P\) on \(c\) and draw the lines \(AP\) and \(BP\). Then determine the second intersection points \(Q\) and \(S\) of these lines with \(c\); the family of lines through \(Q\) and \(S\) has ellipses, hyperbolas or circles as envelopes. After presenting various examples, the author proves this and shows in addition how to find the semi-minor and the semi-major axes (of an ellipse) by Euclidean constructions.