A polarity, π, of a projective plane, P, is an involutory (i.e., of order two) bijection between the points and the lines of P that preserves the incidence relation.
[5] Orthogonal polarities, corresponding to symmetric bilinear forms, are also called ordinary polarities and the locus of absolute points forms a non-degenerate conic (set of points whose coordinates satisfy an irreducible homogeneous quadratic equation) if the field does not have characteristic two.
In characteristic two the orthogonal polarities are called pseudopolarities and in a plane the absolute points form a line.
[8] In summary, von Staudt conics are not ovals in finite projective planes (desarguesian or not) of even order.
[11] However, R. Artzy has shown that these two definitions of conics can produce non-isomorphic objects in (infinite) Moufang planes.