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(CBS News) Joan Rivers remained in a New York City hospital on Friday, one day after going into cardiac arrest at a doctor's office.

Her daughter, Melissa Rivers, released a statement Thursday giving an update on the 81-year-old comedian's condition.

"I want to thank everyone for the overwhelming love and support for my mother," she said. "She is resting comfortably and is with our family. We ask that you continue to keep her in your thoughts and prayers."

The legendary comedienne is in a medically induced coma at a hospital in New York, reports "Entertainment Tonight" co-host Nancy O'Dell, after she stopped breathing while having a throat procedure at a clinic on New York's Upper East Side.

The Mount Sinai Hospital said it had no updates Friday. On Thursday, hospital spokesman Sid Dinsay confirmed that Rivers had been taken there in the morning.

New York City police officials, who spoke on the condition of anonymity because they weren't authorized to publicly name Rivers, said she was taken to the hospital just after 9:30 a.m. Thursday.

The comedian with a half-century of show business under her belt has spawned a reputation for often-snarky red carpet fashion commentary. A show she had scheduled Friday at the Count Basie Theatre in Red Bank, New Jersey, has been postponed.

Rivers spoke at an employee event at Time Inc. in New York on Wednesday night and appeared healthy, practically jogging when she walked in to take her seat, Shira Blum, an online project manager, said Thursday.

"She seemed totally healthy," Blum said. "She was very energetic, hilarious, funny. And it was such a shock, a surprise to hear the news this morning."

Rivers took questions and said she wakes up every morning and "is thankful that everything works," Blum said.

An early and outspoken proponent of cosmetic surgery, Rivers' drastically altered her appearance over the years -- and found plenty of material for jokes. ("I've had so much plastic surgery, when I die they will donate my body to Tupperware.")

The host of "Fashion Police" on E!, Rivers also presides over an online talk show, "In Bed With Joan" and co-stars with her daughter on the WEtv reality show, "Joan & Melissa: Joan Knows Best?"

Her latest book, "Diary of a Mad Diva," was released this summer.

In 2009, Rivers emerged as the winner of NBC's "The Celebrity Apprentice." A documentary, "Joan Rivers: A Piece of Work," premiered in theaters in 2010.

The New York native originally entered show business with the dream of a theatrical career, but comedy became a way to pay the bills while she auditioned for acting roles.

"Somebody said, 'You can make six dollars standing up in a club,'" she told The Associated Press in 2013, "and I said, 'Here I go!' It was better than typing all day."

After proving herself in comedy clubs as a rarity -- a woman comedian -- Rivers was a smash on her first booking on "The Tonight Show Starring Johnny Carson" in 1965. "God, you're funny," Carson told her.

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