3.3. Intersections of C1 with L1 and L2. There is an easy parametrization of points
on the line 1. Since it clearly contains the points (1 : 1 : 1) (the centroid) and
(c2 : a2 : b2), every point on L1 is of the form (c2 + t : a2 + t : b2 + t) for some
real number t. Direct substitution shows that this point lies on the conic C 1 if and
only if