The High Court is deciding whether a man can take his chronically-sick wife to Switzerland for an assisted suicide.
Assisted suicide is not illegal in some other countries
The woman, who has a progressive brain disease, is too ill to travel alone and would need someone to help her.
The court is being asked if her local council should stop others taking her to a country where euthanasia is legal.
Euthanasia campaigners say the case will clarify the law, but opponents argue that helping people to leave the country to commit suicide is illegal.
At present, the woman, who was diagnosed with cerebellar ataxia in 1997, is receiving care at home from her local authority.
Mark Everall QC, representing the local authority, told Senior Family Division judge Mr Justice Hedley that the husband was at first reluctant to help his wife end her life.
However, as her condition worsened, he started to make inquiries about the possibility of travelling to Switzerland, where there is no law preventing assisted suicide.
In the UK helping a person to commit suicide can result in a jail term of up to 14 years.
However, the law on helping someone to travel to a country where they could receive help to end their life is unclear, said Mr Everall.
"The husband has stated his view about it - that he will now comply with his wife's wishes.
"The adult children of the family are again in a similar position - while clearly not wishing such a thing to happen, they support their mother in the decision she has taken."
The judge imposed a temporary worldwide injunction in private last week preventing the husband from taking his wife to Switzerland.
He said he had asked for the case to be heard in public because it raised issues "that ought to be the subject of proper public discussion".
But he has made orders banning identification of any of the parties, including the local authority involved and the local police force.
The Voluntary Euthanasia Society (VES) has welcomed the case, arguing the law needs to be clarified.
HELPING PATIENTS DIE
Physician-assisted suicide: A person wishing to die takes their own life with the indirect help of a doctor, for instance by providing prescription drugs
Voluntary euthanasia: A person wishing to die is directly helped to do so by a doctor
But the Pro-Life Alliance said no clarification of the law was needed.
Anthony McCarthy, of the Linacre Centre for Healthcare Ethics, said: "We are talking about sanctity of life, which is fundamental to a just society, and an attempt to undermine that by a woman who is distressed by her condition."
Alistair MacDougall, chief executive of support group Ataxia UK, said: "I can understand how people can easily get to the point of despair and where they don¿t want to carry on.
"People have been active, at the top of their careers. They often see their whole world crumbling, and they feel life isn't worth living."
Non-profit organisation Dignitas runs a centre in Switzerland which has helped about 150 people end their lives.
Euthanasia is not illegal in Switzerland but the facility has become the centre of a row over "suicide tourists" travelling from countries where the practice is illegal.