The imaginary domains of conics and their interpretation in the complex plane (1912)
Wilson, Charles Richard · leaf 210
, respectively. First, let x2 > b2. Then y = ± ^ i Vx2 - b2 By transforming this equation by means of the equationsx = u and y = i v, we get v = +_ ^ /u2 - b^, which may be written in the form a2u2 . D2 v2 . a2b2 = o or u2 v2 b2 a2 This is the equation of a system of hyperbolas with itsfoci on… … 100 101 we get u = £ ~ /v2 - a2, which may be written in the form b2v2 - a2u2 - aV= 0 , or 4- - = 1. a2 b2 This is the equation of a system of hyperbolas with its fo-ci on the v - axis, where 2 a is the transverse axis and 2 b theconjugate axis. (Fig. 21). Therefore, we see that the imaginary…
Conic sections · Geometry, Analytic · Theses
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