The imaginary domains of conics and their interpretation in the complex plane (1912)
Wilson, Charles Richard · leaf 202
vely.First, let x2>a2Then y = ± il/x2 - a2. Transforming this equation into the complex plane, by means of the equations x = u and y = i v, / p o we get v = ±V m - a.* , which may be written in the form u2 - v2 - a2 = 0 u2 v2or .Z_ =1. a^ a^ This is the equation of a system of equilateral… … 97 we get u = ±\fv2 - a2, which may be written in the form 2 2 2 _ v2 u2 , v - ufi - a =0 or I. - ^ : 1, a^ This is the equation of a system of^lateral hyperbolas,whose axis coincides with the v - axis (Fig. 19). Therefore, we see that the imaginary domains of a circlein the real plane, map into…
Conic sections · Geometry, Analytic · Theses
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