The imaginary domains of conics and their interpretation in the complex plane (1912)
Wilson, Charles Richard · leaf 214
stem of real hyperbolas, with their centers at the origin and foci on the x - axis. But if x2 «< a2, we get imaginary value8 for y. Let x2< a2 Then y = + | i /a2 - x2. By transforming this equation by means of the equationsx = uand y = i v, we get v = _+ a /a - u , which may be written in the… … 103 letting x2< b2, and transforming by the same equations, we get a2u2 + b2v2 - a2b2 = 0, which is the equation of a system of ellipses with its foci on the v - axis (Fig. 24). 2 2 Then take the equation ^ - * = 1. b a^ When y2 b2, this equation represents a system of real hyperbolas with the…
Conic sections · Geometry, Analytic · Theses
Internet Archive · University of Illinois Urbana-Champaign · Public Domain Mark 1.0. Free to use for anything.
