The imaginary domains of conics and their interpretation in the complex plane (1912)
Wilson, Charles Richard · leaf 206
lues for y or x, respectively. 2 p First, let x > a . Then y = + - i /x - a.— a By transforming this equation into the complex plane, bymeans of the equations x = u and y = i v, we get v = _+ -l/u^ - ,2 a-r - 3l t which may be written in the form 2 2 . o 2 p 2 u2 v2 a^v - b2^ + a2b =0 or —2 ~ p-… … Fig. 20. 99 By transforming this equation into the complex plane, bymeans of the equations x = i u and y = v, we get u = + - ]/v2 - b2, which may be written in the forma2v2 _ b2u2 _ a2b2 = 0> or _ ^ = 1. This is the equation of a system of hyperbolas with itsfoci on the v-axis, where 2 b is the…
Conic sections · Geometry, Analytic · Theses
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