Some Equations Connected with the Plane Section of the Conicoid

Extract

We propose in this paper to develop equations which give the principal points and lines of the conic formed by the intersection of the general conicoid.

S=ax²+by²+cz²+2fyz+2gzx+2hxy+2ux+2vy+2wz+d=0,

with the plane lx+my+nz+p)=0, in a form convenient for numerical work. We discuss the general case in which special values of the constants do not lead to special cases the slight modifications necessary where such occur become clearly manifest in numerical work. For brevity, the expressions ax+hy+gz+u, etc., will be denoted by the usual symbols X, Y, Z, and for nY - mZ, lZ - nX, mX - lY we will write U, V, W where lU + mV + nW≡0. We can assume without loss of generality that n is not zero.