Does Islamic law permit euthanasia for a person who is no longer hoped to be cured from an illness?

Fatwa, posted 4.22.2010, from Egypt, in:
Religious Authority: 
Ali Gomaa
Fatwa Question or Essay Title: 
Does Islamic law permit euthanasia for a person who is no longer hoped to be cured from an illness?

Islamic law does permit the removal of the medical equipment utilized to keep a person alive when it is no longer hoped that such a person will be cured and no progress is being made in the attempt to restore their health--due to being "clinically dead"--only when physicians advise to do so. If, however, the equipment has another purpose, like the removal of fluid to improve respiratory health, it is not permissible to deactivate them. This is different, though, from what is called "euthanasia" wherein the sick person requests from the physician to end their life or when the physician decides that unilaterally due to some handicap that will afflict the sick or because of severe pain. Such decisions are unequivocally unlawful because the sick is still living and their life is not dependent upon the life preserving equipment. Rather, the only concern is that the sick or the physician desires to put an end to life due to the excessive pain experienced by the sick. To end life in such an instance will be considered homicide and a murder of a soul that God has declared sacred.