**Proposition 11.2.6**: *A Ganley type flock is a flock of a quadratic cone.*

*Pf*: Let q = 3^{n}, and F = F(t^{3},t,t^{9}). To show that this flock is a flock of a quadratic cone, we must find a conic in the complement of the baselines of the flock. The baselines of F are the lines in W = 0 satisfying the equations t^{3}X + tY + t^{9}Z = 0 for t0 in GF(q). Consider the conic in W = 0 given by X^{2} + mYZ -m^{3}Z^{2} = 0, where m is any non-square in GF(q). The conic is in the complement of the baselines if, and only if, X^{2} + m(-t^{2}X -t^{8}Z)Z -m^{3}Z^{2} = 0 has no non-trivial (i.e., X = Z = 0) solutions in GF(q). This quadratic equation has no non-trivial solutions provided (-mt^{2})^{2} - 4(-mt^{8} -m^{3}) is a non-square for all t0. Now,

= m(t