A 54-year-old Michigan woman, distressed by her father's mental deterioration, apparently decided to end her family's anguish by killing the 84-year-old patriarch and then herself outside the Washington Hilton Hotel, family members and friends said yesterday.

Beth Lois Katz, of East Lansing, Mich., shot her father, Robert O. Shaw, twice in the head with a .38-caliber revolver while the two sat in her station wagon Wednesday night, police said. The elderly man's body was found slumped in the front passenger seat; his daughter, who was suffering from a single gunshot wound to the head, was found behind him in the rear seat.

She was taken to George Washington University Hospital, where she was pronounced dead a half-hour after the shootings.

The twin tragedy affected a family with deep roots in the small town of Exeter, N.H. Shaw, a lawyer, was a fixture in the community and an outspoken activist in a place known for the famous prep school. Beth Katz, one of three daughters, was described by friends in East Lansing as vivacious and kind-hearted, a mother of two who made a living out of staging puppet shows and had an abiding interest in the peace movement and the environment.

Family members struggled yesterday to understand how a woman who was known to be very close to her father set out to kill him.

"From what we are able to figure out, she felt that this was the most humane option for him," David Katz, her former husband, said in a telephone interview from East Lansing. "She never mentioned this to anyone. We had no idea. This came as a complete surprise to us."

"This is a tragedy," said Beth Katz's 24-year-old son, Aaron. "She had the best intentions in mind. She just made a mistake."

For the last two months, Shaw had been living with his daughter Peg in her Dupont Circle home. He was on a waiting list to enter a nursing home in Brentwood, N.H., but family members disagreed about whether he would go. On Saturday, Beth Katz traveled from Michigan to visit her father and sister. She was expected to stay a week.

Family members believed Shaw suffered from Alzheimer's disease, which afflicts about 4 million Americans. More than seven out of 10 sufferers live at home, cared for by relatives who cope with the often extraordinary hardships presented by the disease.

"The immediate family did everything they could to keep him within the family," said David Katz. "But there was a sense that they were running out of time and that institutionalization was the only alternative." Of his former wife, Katz said, "She was deeply distressed at the prospect that he would be institutionalized."

Peg Shaw, a Washington lawyer, said her father had suffered profound hearing and memory loss and was undergoing diagnostic tests. "My sisters and I had differences of opinion, I think, on whether he was suffering a great deal," she said. "We were trying to build a life for him here that was one he could live."

Peg Shaw said her father still led a vigorous life. He had walked a mile the day before and had gone to a driving range. The night before he died, he read her a chapter from William Manchester's "The Glory and the Dream," a history of the United States from 1932 to 1972, Peg Shaw said.

In Exeter, one hour north of Boston, Shaw was a prominent citizen and successful lawyer handling income tax work, personal litigation and divorces before retiring in the mid-1980s. His illness was widely known but seldom mentioned in town, said Robert M. Swasey, a neighbor of Shaw's on Drinkwater Road and an acquaintance for 52 years. Sometimes it caused problems.

One time, after a squabble with his wife, Shaw set out for a bakery but got lost, Swasey said. Neighbors found him and took him to police.

Beth Katz kept in regular touch and visited her father at least twice a year, friends say. She was a very caring person and extremely close to her father, friends said.

Beth Katz had an active career, putting on one-person puppet shows at birthday parties and public libraries and conducting writing seminars at schools for staff and children. Her work took her around Michigan and to other states, including Indiana, Illinois and Massachusetts.

"She seemed to get a lot of satisfaction from her work," said Liz Signell, a close friend and neighbor in the Midwestern college town. "She was very interested in getting teachers to write more. She felt if kids didn't write, they wouldn't read."

About 12 years ago, at her own doing, Beth Katz divorced her husband, Signell said. In recent years, she rented a room to students from Michigan State University, where her ex-husband is an associate professor of social work. She was a "most generous person with her money, which she didn't have a lot of," Signell said. "She would pick up people who had signs `I'll work for food' . . . and have them work in her yard."

Two years ago, Signell recalled, Katz's purse was stolen at Sparrow Hospital in Lansing where she was undergoing tests. "She said: `Well I'm not going to get upset. They must have needed it more than I did,' " Signell said.

"Her father had been the most amazing person in her life," Signell said. It was her fondness, her closeness, that caused such angst, friends and family said.

After 12 years of marriage, Shaw's second wife, Elizabeth D. Shaw, asked his three daughters to spend some time caring for him, family members said. His condition had deteriorated. "He had his doubts about whether he wanted to live," David Katz said. "He had expressed some suicidal tendencies."

For a while, Shaw stayed with a third daughter, Ronney Nadile, in Massachusetts. Two months ago, it was Peg Shaw's turn. Beth Katz arrived Sunday. On Wednesday night, she and her father drove around in her Ford Taurus station wagon. Shortly before 9 p.m., they pulled up into the circular drive of the Washington Hilton.

Police said Beth Katz exited the station wagon, sat in the rear and shot her father twice in the back of the head. She then turned the gun on herself.

"It's very possible we'll never know" her motivations, said Jose Acosta, the commander of the 3rd Police District. He said a mercy killing is "is certainly a theory we're looking at." Acosta said the gun had been bought in Michigan.

Friends and acquaintances were shocked not only by the news but also by the circumstances of the deaths. "I think having a gun or handling a gun would have been pretty foreign to her," said Sylvia Marabate, director of the East Lansing Public Library, which Katz frequented, sometimes to buy used books for inner-city children. Echoed neighbor Susan Kalvonjian: "Good Lord, I would be incredibly surprised that she ever touched [a gun]. I'm shocked."

All tried to make sense of what happened. Signell said Beth Katz felt strongly about keeping her father out of a nursing home. "That accounts for what she did, but that doesn't mean she had to take her life," she said.

In Exeter, a town of 13,500, news of the shooting stunned residents. "He was most known for his interest in protecting the common man at town meetings," said the Exeter town manager, George N. Olson. "You could always guarantee that Bob would stand up at some point and make a very eloquent speech in support or opposition to something in the town warrant for that evening."

Alzheimer's disease affects judgment and concentration, causes loss of speech and alters personality. The disease is incurable, its progress irreversible. The "loss of personae itself is an enormous hardship," said Leonard I. Pearlin, a sociologist and senior research scientist at the University of Maryland at College Park, who has studied relatives of Alzheimer's sufferers. Even a child not immediately involved will feel "a great deal of burden. There's a contagion of stress," he said.

Conflict over who is doing enough, or what the right course of care is, often surfaces. Pondering Wednesday night's shooting, Pearlin said, "My guess is it was not an act borne of the moment but of a history of circumstances that led up to it."

While expressing shock at what happened, Katz's family said theirs is a private anguish. "My ex-wife does not require posthumous rehabilitation," David Katz said. "She did what she did for her reasons."

Staff writer Susan Levine and Metro researcher Bobbye Pratt contributed to this report.