Euthanasia

I was talking Pastor Brad about the Schiavo case and the subject of Euthanasia. My assertion was that now that we have pulled the feeding tube and water, we have effectively killed her. Giving that we have killed her, would it not make sense to kill her quickly rather than slowly? I suggested euthanasia as a viable option, only to find that the act of removing her feeding tube was considered passive euthanasia. The correct term is active euthanasia. I would actively euthanize my dog if he were brain dead; it is the humane thing to do. I would not want to see my dog suffer any unnecessary pain, should we not feel the same way about Schiavo? Comments?