Is mercy killing right?

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Few countries have legally permitted the mercy killing,i.e. to let die the sufferer peacefully by his or her consent because of agonoizing life.People who are physically bed ridden or are suffering badly, either they ought to be given the death by mutual consent or not as per their wishes? If this silence death is provided to give shy of releif to the patient,Is that right?.. If so ,then why? and what is the safest mode to give that death?