General Electric Co. and Atlanta-based Cox Broadcasting Crop. announced yesterday that the two companies are entering into negotiations "of a definite agreement for combining Cox Broadcasting with General Electric's radio-and-television broadcasting and cable-television business."

Because both companies have substantial broadcasting properties, the merger - if completed - would require the sale of three VHF TV stations, at least one AM radio station, and five FM stations to meet Federal Communications Commission ownership limitations rules.

The announcement that GE, the world's largest diversified industrial company and Cox, one of the country's most profitable and highly-regarded broadcasting companies, may merge came as a complete surprise to Wall Street analysts who follows the two firms. The stock deal would be approximately $450 million and reportedly would be the biggest broadcast deal in history.

There was meanwhile some speculation that a third company might come in and make a tender bid for Cox.

The rationale behind the proposed GE-Cox merger appeared to be two-fold:

To eliminate the media cross-ownership problems for the Cox family which holds nearly half the shares of Cox Broadcasting, and also separately owns all of Cox Enterprises, which has newspapers in a number of cities, including Atlanta and Dayton where there also are key Cox Broadcasting properties.

Garner Anthony, chairman of Cox Broadcasting's executive committee, said a major factor behind the combination under consideration is "the increasingly regulatory pressure on common ownership of different media in the same market area."

To combine the extensive cable television operations of both GE and Cox and apply GE's financing cable business. GE now operates 12 cable systems with a total of 170, 000 subscribers. Cox Broadcasting through its cable subsidiary operates 44 cable systems with a total of 550,000 subscribers.

"We've looked positively at the cable business ever since the early 1960s," said Cox Broadcasting President Clifford Kirtland Jr., "and we think it's the next major evolution for entertainment in the home."

He said the two companies first approached each other a month ago and "it was as close to a mutual get-together as you can have. There was a recognition on our part that we needed to do something to relieve the cross-ownership pressure. And there was a recognition at GE that they would like to expand in broadcasting and cable."

GE Chairman Reginald Jones, prior to addressing a special shareholders meeting for the company's 100th birthday celebration, noted that "General Electric has been a pioneer in radio and television broadcasting."

GE has had a long history in telecommunications, being responsible for some of the key technical developments that made radio possible. It owned some of the earlest broadcast properties. And, at the urging of the U.S. government, GE and American Telephone & Telegraph in the early 1920s took over the American Marconi Co. and formed the Radio Corporation of America.

But for GE, broadcasting has not been as important over the years as a source of revenue and income as it has been for arch electronics rival Westinghouse, which has a very strong and profitable broadcasting division.

If the negotiations are successful and the requisite regulatory approvals are obtained, two socially and politically prominent Atlanta sisters, Barbara Cox Anthony and Anne Cox Chambers could end up as perhaps the largest single shareholders of GE.

With a total of 720,000 subscribers, that would form the second largest cable television company after Tele-Prompter.

With ownership of "somewhat over 40 percent of Cox Broadcasting" according to the company, the sisters would wind up with approximately 3.5 million shares of GE, worth nearly $250 million at current market values. But with about 230 million GE shares outstanding, the Cox family holdings would still amount to just 1.5 of GE's stock.

The Cox family has a long link to national politics going back to when Ohio Gov. James Cox ran for president as the Democratic nominee against Warren Harding in 1920. Cox's running mate was Franklin Roosevelt.

Mrs. Anne Cox Chambler was a leading supporter of Jimmy Carter in the 1976 bid for the presidency. And she is currently the U.S. ambassador to Belgium.

The directors of the two companies have authorized negotiations to proceed on the basis of a tax-free exchange of 1.3 shares of GE common stock for each share of Cox stock, provided that in no event will Cox shareholders receive less than $65 nor more than $72 worth of General Electric stock each Cox share.

At current market values, the formula would result in the issuance of an aggregate of approximately 8.8 million GE shares worth about $467 million. The minimum dollars of the transaction under the formula would be $440 million, and the maximum about $488 million.

GE's stock closed down at a quarter to 52 1/2 on the New York Stock Exchange yesterday. Cox Broadcasting was up 10 1/4 at 59 3/4.

Cox Broadcasting last year earned $25.5 million on operating revenues of $186.4 million. It has broadcast properties in Atlanta, Charlotte, Dayton, Pittsburgh, San Francisco, Los Angeles, Miami, Philadelphia and Baltimore. In addition to the already mentioned cable properties, it has an automobile auction firm, some business publishing interests and a small movie production company in Los Angeles, called Bing Crosby Productions. The movie company's best-known hit was "Walking Tall," the story of Tennessee lawman Buford Pusser.

GE has stations in Albany/Schenectady/Troy, Denver, Nashville, Boston and San Francisco.

GE is the eighth largest U.S. industrial firm with sales last year of $17.5 billion and profits of $1.1 billion. It is the most diversified industrial firm for its size. With interests in consumer appliances, turbine and power generation equipment, engineered plastics and materials, transportation equipment and natural resources.

GE's last major acquisition took place in 1977, when it purchased Utah International - a coal and minerals company - for $1.6 million in what still stands as the largest single deal ever.

Over the years most of GE's growth has been internal. But in 1892 the then Edison General Electric Company merged with the Thomson-Houston Co., which developed alternating current, to form GE. And in 1918, a major consolidation of the budding home appliance business took place when the heating device section of GE merged with the Hughes Electric Heating Co. and the Hotpoint Electric Co. to form the Edison Electric Appliance Co.

The proposed GE-Cox merger still must be negotiated to the mutual satisfaction of the two companies, get approval from the Cox shareholders, and clear regulatory hurdles at the FCC, the Federal Trade Commission and , perhaps, the Justice Department.

"We wouldn't go ahead with this if we didn't think we'd get the necessary approvals," said Cox President Kirtland. "But it may take some time," he added.