Special cubics and quartics produced by projective pencils of straight lines and conics (1916)
Marshall, Robert Haskell · leaf 48
hows that two branches pass through the origin and the slopesof the tangents at the origin are 1 and -1. To construct the locus of the above equation lay offtalues of X on the x axis. Construct the cissoid corresponding toeach value ^ given to A » Also draw lines through the points(0,1) and (AiO),… … 18- to find two pencils whose product vTill give the equation. Suppose the equation x^ —4xy (7 ) is Riven, and it is desired to find two pencils whose product will g-ixe the equation (7), Writing (7) in the form (x^—Hy) —y(i:x^—-^0, it is at once seen that the folloi?;ing- two pencils x-£yAy -0),…
