  We study properties of the convex hull of a set $S$ described by quadratic
inequalities. A simple way of generating inequalities valid on $S$ is to take a
nonnegative linear combinations of the defining inequalities of $S$. We call
such inequalities aggregations. Special aggregations naturally contain the
convex hull of $S$, and we give sufficient conditions for such aggregations to
define the convex hull. We introduce the notion of hidden hyperplane convexity
(HHC), which is related to the classical notion of hidden convexity of
quadratic maps. We show that if the quadratic map associated with $S$ satisfies
HHC, then the convex hull of $S$ is defined by special aggregations. To the
best of our knowledge, this result generalizes all known results regarding
aggregations defining convex hulls. Using this sufficient condition, we are
able to recognize previously unknown classes of sets where aggregations lead to
convex hull. We show that the condition known as positive definite linear
combination together with hidden hyerplane convexity is a sufficient condition
for finitely many aggregations to define the convex hull. All the above results
are for sets defined using open quadratic inequalities. For closed quadratic
inequalities, we prove a new result regarding aggregations giving the convex
hull, without topological assumptions on $S$.
