The imaginary domains of conics and their interpretation in the complex plane (1912)
Wilson, Charles Richard · leaf 110
y + 2 dx + e = 0 or = --g- x - b , which is the equation of a system of parabolas and which may be put in the form (1.) y2 = 4p(x - oc), where <* is the intercept on the x- axis and 4p the latus rectum. Take the equations of a and b as(2.) a_=y-mx+mk = 0 (3.) b=y+mx-mk = 0,. in which m and k are… … Fig. II. ^ 51 4£ ± l/i§EL + 16pk - 16pocy = m — 1/ y _ 2£ ± £ y/p2 + pkm2 - poem2 . But since (2.) is tangent to (1.), the two values of y must be equal. 2£ + 2 \/p2 + pkm2 - pocmd = Sfi. . 2 \JV2 + pkm2 - p<Xm2.mm m |/p2 + plan2 - p*m2 = 0, o 2p + km^ - <* m = 0 , p = m2( o( -k).…
Conic sections · Geometry, Analytic · Theses
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