The Learning Channel, a Washington cable program service, yesterday said it was selling a 47.5 percent stake in the company in the form of 200,000 shares of newly issued common stock to a New York business development company.

As part of the agreement in principle, Biotech Capital Corp. has an option to acquire up to 51 percent of The Learning Channel. Officials of The Learning Channel would not say how much the transaction was worth, but in its fiscal year 1985, ending Sept. 30, the company generated revenue of $3.9 million.

The Learning Channel provides programming on business and career development, parenting and teaching, leisure-time skills and other cable television programming via its own satellite network to more than 670 affiliated cable systems that reach more than 6.1 million homes throughout North America.

Harold E. Morse, company chairman, said the company could now afford to expand its programming to 20 hours instead of 10 hours a day as well as lease more satellite capacity to reach a wider audience.

John Koonce, spokesman for Biotech Capital Corp., said BCC agreed in principle because the company was "very impressed with the management group there; we think it's a good deal."

BCC, a publicly traded company on the New York Stock Exchange, provides capital to, and frequently manages, new and emerging companies. BCC's total assets at the end of its 1985 fiscal year, last June, were $25 million. The company holds major positions in six publicly held firms -- American Cytogenetics Inc., Clinical Sciences Inc., Environmental Processing Inc., Financial News Network Inc., Hadron Inc. and Immucor Inc.

Until recently, The Learning Channel served as a trade name for a D.C. not-for-profit company called The Appalachian Community Service Network. But to attract capital to expand its programming and lengthen its programming hours, the company spun off most of its assets into a privately held company called The Learning Channel, said company officials.

The company will remain privately held with the not-for-profit parent holding 47.5 percent of the assets, Biotech Capital Corp. holding another 47.5 percent of the assets, and the remaining assets held by The Learning Channel Chairman Morse, President Robert Shuman, and Senior Vice President and Chief Financial Officer Henry Schlenker.