On the intersection of a Hermitian curve with a conic

Let ${\mathcal{H}}${\mathcal{H}} be a Hermitian curve and let Γ be a conic of PG(2, q ²). In this paper we determine the possible intersection configurations between Γ and H{\mathcal{H}} under the hypotheses that Γ and H{\mathcal{H}} either share two points with the same tangent lines or contain a common Baer subconic. Moreover, the intersection configurations between a degenerate Hermitian curve and a conic sharing a Baer subconic are also determined.