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The imaginary domains of conics and their interpretation in the complex plane (1912)
Wilson, Charles Richard · leaf 148
k4 - a2k2 + b2k2 + k2^ - k2?2 = 0 ,x2y2 + k2x2 - 2abxy - k2^ + a2b2 - k4 - a2k2 * b2k2 = 0.Solving first for y and then for x, y , abx va2b2x2 - (x2 - k2)(a2b2 - k4 - a2fc2 * b2k2 * k2x9 )and x = aby * \/a2b2y2 - (y2 + k2)(a2b2 - k4 - a2k2 * b2k2 - k2y2) (y2 + k2) Therefore, by this transformation… … Fig. 15. 70 4(ab - xy)2 - 4k4 * 4k2(a2 - b2 - x2 * y2) - 0-a2b8 - 2abxy -»• x^y2 - k4 + a2k2 - b2k2 - k2x2 * k2y2 = 0x2y2 - k2x2 - 2abxy •» k2y2 + a2h2 - k4 •* a2k2 - b2k2 = 0.Solving first for y and then for x, we get v a abx + 7a2b2x2 - (x2 4 k2)(a2b2 - k4 4 a2k2 - b2k2 - k2x2) (X* + k2) and x =…Conic sections · Geometry, Analytic · Theses
Internet Archive · University of Illinois Urbana-Champaign · Public Domain Mark 1.0. Free to use for anything.
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