On some geometric properties and applications of conformal rational transformations in a plane (1912)
Renich, Mary Emma · leaf 28
general equation of a conic, ax8 + 2bxy + cy8 + 2dx + 2ey +f s0,represents a degenerate conic; that is, two intersecting lines,is that the determinant vanishes. Setting up the discriminantof our pencil of conies,.we have, *i +Aa8 bx +A*>2 dx +Ad8 el + A = 0 ^! + A^a ci + Aca *i +Ad8 ei + Ae2 *i… … Returning to our particular equations,-rj« - Cl= 0 and 2^T| - c2 = 0, we have as theequation of the pencil of conies through their intersections, tworeal and two imaginary, £8 + 2A^-rY» -Ci-Ac2 = 0 The values of \ for which (15) represents degenerate conies are *2I A 2* +i» A3= -i. Substituting…
