Hyperovals and Unitals in Figueroa Planes

In [3], W. M. Cherowitzo constructed ovals in all finite Figueroa planes of odd order. Here a class of hyperovals is constructed in the finite Figueroa planes of even order. These hyperovals are inherited from regular hyperovals in the associated desarguesian planes. It is also shown that all Figueroa planes of finite square order possess a unitary polarity, and hence admit unitals.