American Capital and Research Corp., a rapidly growing environmental and engineering company based in Fairfax, said yesterday it has formed a joint venture with an investment banking company owned by Canada's Belzberg family to pursue environmental business opportunities.

The new entity, which is to be funded equally by the two companies, will be called Environmental Industries Inc. and will look for opportunities in waste treatment, recycling, environmental monitoring and controls and other areas, the companies said.

The venture combines the capital-raising abilities of First City Financial Corp. with the environmental expertise of ACR, officials of both companies said. Samuel Belzberg, chairman and chief executive of First City Financial, is also on the board of ACR and his family owns 500,000 shares of the Fairfax company.

First City has been interested in investing in the environmental industry for some time because of the field's potential, Belzberg said.

"We think the people at ACR will help us find the right projects," said Robi Blumenstein, senior vice president of First City Capital, First City Financial's New York merchant bank. "We set up an arrangement that provides a framework to get going. You can talk about these things forever, but we decided rather than talking about things on a hypothetical basis, to get going."

ACR, which went public last October, is an aggressive player in the business of providing studies, engineering and construction management to clean up or improve hazardous waste sites. James O. Edwards, ACR chairman and CEO, said the joint venture also may provide markets for some of the firm's other businesses.

"We thought it would be a good combination if we took our knowledge of the environment ... and married it to their large-scale availability of capital and deal-making capability and connections in Canada and elsewhere in the world to create a company or group of companies that could make some money in this booming market in the next couple of years," he said.

ACR itself has grown rapidly in recent years, acquiring 13 companies in the past three years, including Kaiser Engineers of Oakland. Last week, it reported a 66 percent increase in its fiscal first-quarter earnings, to $2.8 million (15 cents a share), from the same period a year ago. Its revenue rose from $57 million in fiscal 1987 to $500 million in fiscal 1990, ended Feb. 28.

ACR's stock closed yesterday at $14.25, down 37 1/2 cents.