The imaginary domains of conics and their interpretation in the complex plane (1912)
Wilson, Charles Richard · leaf 192
lines, x f parallelto the y-axis and having negative values of x,are transformed intothe equilateral hyperbolas, x , in the w-plane, whose transverse axis has the ai r>r^2 + b2 - a (Pig# 18)# b Then Third, let z describe the straight line y = +k.2auv-bu2 + bv2 m ^ a2 ■*• b2 bv2 - bu2 4 2auv = k(… … 92 b -\/a2 + b2 axis has the slope (Pig. 18). a Fourth, let z describe the straight line y « -k, Then bv2 - bu2 4 2auv * -k(a2 + b2), or bu2 - bv2 - 2auv « k(a2 + b2). Therefore, by this transformation, the lines, y parallelto the x-axis and having negative values of y are transformed intothe…
Conic sections · Geometry, Analytic · Theses
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