  This article studies conics and subconics of $PG(2,q^2)$ and their
representation in the Andr\'e/Bruck-Bose setting in $PG(4,q)$. In particular,
we investigate their relationship with the transversal lines of the regular
spread. The main result is to show that a conic in a tangent Baer subplane of
$PG(2,q^2)$ corresponds in $PG(4,q)$ to a normal rational curve that meets the
transversal lines of the regular spread. Conversely, every 3 and 4-dimensional
normal rational curve in $PG(4,q)$ that meets the transversal lines of the
regular spread corresponds to a conic in a tangent Baer subplane of
$PG(2,q^2)$.
