The imaginary domains of conics and their interpretation in the complex plane (1912)
Wilson, Charles Richard · leaf 168
lel to the v-axis, u^, in the w-plane are transformed into thequartics, u* , in the z-plane, each of which always has twobranches, Pig. (16). By this transformation, as in the preceding one, in generalthe curves u^. are orthogonal to the curves v^, for the lines u^are orthogonal to v^ in the… … 80 We have w - (3 •Then U4iv ■ 4jc + id). u = c, v * + d . How, let w describe either of the straight lines v = 4_ d.From I, B2 - 4d* - 4d2A = 0 From (3) , and (4) , and remembering n = d2 - c2 and p = -cd,m2*4 - 21mx3y 4 (l2 - 2m2)x2y2 - 21mxy3 4 m2y4 - (amp 4 d2l)x2+(4rad2 - 21p)xy + (2mp 4…
Conic sections · Geometry, Analytic · Theses
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