  We consider a non-degenerate conic in $\PG(2,q^2)$, $q$ odd, that is tangent
to $\ell_\infty$ and look at its structure in the Bruck-Bose representation in
$\PG(4,q)$. We determine which combinatorial properties of this set of points
in $\PG(4,q)$ are needed to reconstruct the conic in $\PG(2,q^2)$. That is, we
define a set $\C$ in $\PG(4,q)$ with $q^2$ points that satisfies certain
combinatorial properties. We then show that if $q\ge 7$, we can use $\C$ to
construct a regular spread $\S$ in the hyperplane at infinity of $\PG(4,q)$,
and that $\C$ corresponds to a conic in the Desarguesian plane
$\P(\S)\cong\PG(2,q^2)$ constructed via the Bruck-Bose correspondence.
