A characterization of the sets of internal and external points of a conic

We provide a characterization of the sets of internal and external points of a nondegenerate conic in the plane PG ( 2 , q ) , q odd, by means of their pattern of intersection with lines. In fact, we classify all sets of class [ 0 , 1 2 ( q − 1 ) , 1 2 ( q + 1 ) , q ] in PG ( 2 , q ) , q odd.