Would you kill someone because they asked you to do so?

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Well, most people would want to live long. But there are people who would want to end their life as soon as possible. Who I am talking about here is the people terminally ill or in vegetable state. Euthanasia is the practice of ending someone's life to relieve the pain and suffering that person suffers. It could be with this person's knowledge or not. In people under coma and doctors feel hopeless, this thing is suggested. If the person lives because of the machines attached to his body, the doctor will ask you and make you sign if you agree a statement saying that you or someone you allow would turn that machine off and therefore ending the supply of life for that person. Then he dies. Euthanasia have always been a moral debate. Though this thing depends on someone's decision, other people would find it to be morally illegal while others would think it is fine. This practice is being done for several reasons. One of those reasons is that the people under this situation are HOPELESS. They are dying or will die, and that one person will just hurry the dying progress. Another reason is financial stress. As most of these people are hopeless, some find it unreasonable to spend too much money to try to cure them when they are actually cureless. If you're on this situation (a love ones is dying and the doctors or the patient himself is asking you to do this), how would you respond?