The imaginary domains of conics and their interpretation in the complex plane (1912)
Wilson, Charles Richard · leaf 98
2 2A p g C C k = any positive number. ;2 1. LetX/3g = - k. From (2.), * t * x2 + LLL y2 + 1 = 0,- kc c2 or - MgS- = 1, which is the equation of a system of confocal hyperbolas, with fo-ci at P^ (c , o) and Fg (-c , o) as shown in Fig. (9). 2 / x 2 From (1.) , x = 0, which is the degenerate conic,… … 45 4. Let A (3| = 1. From x2 + A(32 y2 ♦ Mis! = o, IfA [31 approaches 1 in the ascending order of the number system, 2 2 x + y +<»= 0» or x2 + y2 = (i«>)2, which is an imaginary conic. If A(32 approaches 1 in the descending order,2 x2 + y2 - oo = 0 , 2 p 2 or x + y = oo , which is a circle…
Conic sections · Geometry, Analytic · Theses
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