The imaginary domains of conics and their interpretation in the complex plane (1912)
Wilson, Charles Richard · leaf 218
a system of ellipses with its foci on the v-axis (Fig. 25). Therefore, we see that the imaginary domains of the two 2 tt2 2 2 hyperbolas in the real plane, ^ - X^. _ i an(j J~ - :L- = 1, map a b b2 a2 into like ellipses in the complex plane. Also the imaginary do- 2 2 mains of the two hyperbolas 2—… … 105 When p>o and x >o, this is the equation of a system of par-abolas, with the vertex at the origin and foci on the positive x -axis. But if x <0, we get imaginary values for y. So, let x <0.Then y = + 2 i /p x. By transforming this equation by means of the equations x = u and y = i…
Conic sections · Geometry, Analytic · Theses
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