  We study containment regions of the numerical range of the product of
operators $A$ and $B$ such that $W(A)$ and $W(B)$ are line segments. It is
shown that the containment region is equal to the convex hull of elliptical
disks determined by the spectrum of $AB$, and conditions on $A$ and $B$ for the
set equality holding are obtained. The results cover the case when $A$ and $B$
are self-adjoint operators extending the previous results on the numerical
range of the product of two orthogonal projections.
