Triángulos simétricos del triángulo preceviano de un punto, perspectivos con el triángulo de referencia

(Paris Pamfilos,)
Triangle A'B'C' is perspective to ABC w.r. to point P. For which points Q, the symmetry S_Q w.r. to Q, produces
A''B''C'' = S_Q(A'B'C') also perspective to ABC?

(Paul Yiu)
Let's take A'B'C' to be the ANTICEVIAN triangle of P.

This conic [locus of Q] is the bicevian conic C(G,P'), where P' is the commonpoint of the circumconics C_P (with perspector P) and C'_P (with center P).