Melissa Hayden, a lyrical, exquisite dancer who performed with the New York City Ballet for more than 20 years, died Aug. 9 after a brief illness. She was 83.Hayden, who was born in Toronto as Mildred Herman and was known to her friends as Milly, started her dancing career in Boris Volkoff’s Canadian Ballet. After a brief stint at Radio City Music Hall, she joined Ballet Theatre, soon becoming a soloist in 1945. But the majority of her principal career took place at the New York City Ballet, where she was a soloist from 1953 to 1954 and a principal dancer from 1955 until 1973. Famed ballet master George Balanchine, who started the company, helped Hayden develop her style — vulnerable yet strong — with roles in “Agon,” “The Figure in the Carpet” and “La Source.” On her 20th anniversary with the ballet, dance critic Clive Barnes wrote: “She has survived and survived, and, more pertinently, she has gotten better and better. New York City Ballet’s Melissa Hayden is its greatest dancer.” When Hayden announced her retirement in 1973, Balanchine created a ballet in her honor, “Cortege Hongrois,” and at the company’s spring gala she was awarded the Handel Medallion, the city’s highest cultural award. Hayden also performed the ballerina role in Charlie Chaplin’s movie “Limelight” and wrote two books, “Melissa Hayden — Off Stage and On” and “Ballet Exercises.” After leaving the New York City Ballet, Hayden went to teach at the North Carolina School of the Arts in 1983 and was teaching until a month ago.