  In this paper, we consider the extended trust region subproblem (\eTRS) which
is the minimization of an indefinite quadratic function subject to the
intersection of unit ball with a single linear inequality constraint. Using a
variation of S-Lemma, we derive the necessary and sufficient optimality
conditions for \eTRS. Then an SOCP/SDP formulation is introduced for the
problem. Finally, several illustrative examples are provided.
