Do you agree in Eutanasia...Mercy Killing?

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I had a friend who's father has been sick for almost a year. Her father got a stroke and on the third time he was comatose, only machines help him to live. Their doctor could'nt do anything but to wait him to wake up, if ever he would wake up. They are now suffering in financial problem because of hospital bills. The doctor suggest that they could end his suffering, since the case is almost hopeless. They could'nt decide because they are talking about their father's live. If you are on the position to decide...would you agree in mercy killing?