A characterisation of <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si1.svg"><mml:msub><mml:mrow><mml:mi mathvariant="double-struck">F</mml:mi></mml:mrow><mml:mrow><mml:mi>q</mml:mi></mml:mrow></mml:msub></mml:math>-conics of PG(2,q3)

This article considers an Fq-conic contained in Fq-subplane of PG(2,q3), and shows that it corresponds to a normal rational curve the Bruck-Bose representation PG(6,q). The main result characterises which curves PG(6,q) correspond via Fq-conics PG(2,q3). interest are called 3-special, property describes how extension meets transversal lines regular 2-spread representation. proof uses geometric arguments exploit interaction between PG(2,q3) PG(6,q), Bose PG(8,q).