Special cubics and quartics produced by projective pencils of straight lines and conics (1916)
Marshall, Robert Haskell · leaf 56
g x^-y^i c —h) =1;^xVy- ^-1 for the two pencils such that their product will give (9). The first poncil will give a series of elipses for values of/\^2. For values greater than 2 a series of hyperbolas. In the second we ^et a pencil of hyperbolas. The lemniscate could be constructed by constructing… … 20- leraniscate. We might say here, that if we have given a certainequation, there are in most cases various projective pencilssuch that their product will give the equation.Let us divide the equation of the lemniscate hy(xVy! (X - y ). We get X /-x -h JX —■ y x-!- y^ If we put these equations…
