Special cubics and quartics produced by projective pencils of straight lines and conics (1916)
Marshall, Robert Haskell · leaf 68
id has the circularpoints as custos. 9. We shall next consider the two pencils x^ + 2y-4x +~ 3 and 4x - A Writing these in the form (x-E)^ f y(2-A) - 1 ( x 2 ^ A 1 - \ 4 -^ A 4 -f A (16) A the first is seen to be an ellipse for all values of /V ^ 2, forvalues of X ^^ pencil of hyperbolas is formed.… … ll dis-positive values of /\ in the second pencil the center of theellipses approach the origin, the vertical axes approach unity-while the horizontal approaches zero. If trie product of the twopencils is formed v/e have after simplifying^ x i- y^-f 2xV 2xy^ -~4x^ - 4xy^-yVq (17 ) Putting y-mx in…
