The imaginary domains of conics and their interpretation in the complex plane (1912)
Wilson, Charles Richard · leaf 116
-<*)(x - <x). 1. When oc < c. The equation represents a system of confocal parabolas for X ^ oc When x<oc, y is imaginary. 2. When oc = c. The equation represents a degenerate parabola, the x-axistaken twice, for all values of x. 3. When c< >c. The equation represents a system of… … 54 . •. take a = P2I]L=y-i(x + c)=0 (7.) and b = P2I2 = Y + i(x + c) = 0 (8.)Comparing (7.) with C2.) and (8,) with (3.), we see m = i andk = -c. Substituting these values in (4.), y2 = (-4c - 4<X)x + 4<X2 + 4cxc.Ill y2 = 4(-c - <x)(x - «) » which is the equation of a system of confocal…
Conic sections · Geometry, Analytic · Theses
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