ABSTRACT
The midpoints of a family of parallel chords of a quadric Q lie in a plane. In order to prove this let the chords be represented by
p = b + vA , where v is fixed and b varies.
The intersection points of one of these chords with Q are found by solving
where a = v ^ v , /? = [Cb + c]tv, and 7 = Q(b). In particular, b is the midpoint of the chord if
which is a linear equation for b = x , concisely denoted as vtx+uo = 0 and called the diametric plane of Q with respect to v. Examples are illustrated in Figure 14.1. A diametric plane V contains all midpoints of Q, i.e., one has M C V. Note that the diametric plane does not exist if v is axial, i.e., if C v = o.
