A budget of inversions (Q1804942)

In the real Euclidean plane, if the a) sum, b) difference, c) quotient or d) product of the distances from two fixed points is a constant, the locus \(c\) is a) an ellipse, b) a hyperbola, c) a circle of Apollonius, or d) an oval of Cassini, respectively. The author first maps the curves \(c\) of these four types a)--d) by the (usual) inversion in a circle cutting \(c\) in two distinct points (thus being fixed points of the mapping). He presents the (well-known) equations and figures of the (algebraic) image curves. Finally he studies the inverses of lines not passing through the center \((0,0)\) of inversion while using the (unit) circle of inversion \(| x| + | y| = 1\) based on the ``city block metric''.