The Fairfax County Board of Supervisors endorsed the design of a vast portion of the Springfield Bypass yesterday, voting unanimously to approve the locations of 18 interchanges and 49 intersections along the proposed 35-mile cross-county road.

In a meeting crammed with a variety of housekeeping issues, the board voted 5 to 2 to endorse the concept of changing the county's zoning ordinance to allow free-standing basketball standards in front yards. But the proposal, made by Supervisor Thomas M. Davis (R-Mason), calls for the standards to be on the side of a driveway farthest from a neighbor's property.

Davis said he believes that existing hoops might be grandfathered in. The county staff was ordered to review the proposed amendment.

Voting to endorse a change in the hoop law, in addition to Davis, were Supervisors Katherine K. Hanley (D-Providence), Elaine McConnell (R-Springfield) and T. Farrell Egge (R-Mount Vernon) and Chairman John F. Herrity (R-At Large). Nancy K. Falck (R-Dranesville) and Joseph Alexander (D-Lee) voted against endorsing the change, and Audrey Moore (D-Annandale) and Martha Pennino (D-Centreville) were absent when the vote was taken.

In other matters yesterday, the board:

Voted to advertise a bill to raise taxi rates by about 24 percent. Under the proposed increases, one passenger would pay $1.20 for the first one-sixth of a mile and 20 cents for each subsequent one-sixth of a mile. Also, passengers would be charged 20 cents for each minute of waiting time.

The cab fare for the average 5.7-mile taxi ride in the county, therefore, would rise from $6.20 to $8 under the proposal. The increases would be the first in six years. A public hearing on the measure has been scheduled for June 29. Voted to cut the county's proposed fiscal 1988 contribution to the Health Systems Agency of Northern Virginia, a regional advisory board that monitors and makes recommendations for changing the mix of health services in the area, from $68,700 to $34,350.

Fairfax officials have long held that the group, which receives funds from local Northern Virginia governments, has a bias against Fairfax. The officials point to the agency's recommendations for reducing health services offered in hospitals in the county while expanding services in hospitals in other jurisdictions.

Voted 8 to 0 to approve funding for a variety of county programs using $3.6 million in federal funding from the Community Development Block Grant program. About $200,000 was targeted for home repair for the elderly, $326,322 for housing relocation, and $777,870 (including $135,000 in county funds) for a home improvement loan program.

Voted 7 to 0 to increase from $100 to $500 the amount people could be fined for having animals that repeatedly are found in violation of the county's leash law.

Voted 9 to 0 to deny a request by developers that it amend the county's comprehensive plan to allow a large office park on 57.5 acres of land adjacent to the Center for Innovative Technology near Dulles Airport. The board's action sets aside the land, located west of Rock Hill Road and North of the CIT and the Dulles Access Road, for housing units at the relatively low density of two to three houses an acre.

The developers, Alan I. Kay and Samir Kawar, who in 1984 gave the state 35 acres on the Fairfax-Loudoun county line for the CIT headquarters, had hoped to build as much as 2.1 million square feet of office space on the property. Although the state had promised to help the developers obtain the necessary zoning, the county has authority over rezonings. Supervisors said last night that preserving the residential character of a subdivision east of the 57 acres was their primary concern.

The action taken yesterday on the Springfield Bypass came after a series of hearings in which the public was allowed to comment on the proposed path of the road. Those comments were used in drafting the design plan approved yesterday, and the plan will be forwarded to the Virginia Department of Transportation, which has final say.

One of the main concerns voiced by supervisors and the county staff yesterday was whether the state would conduct a noise study along the entire route of the bypass -- or only sections of it -- to determine what kinds of buffers will be needed.

The county has proposed that the state establish "specific policies and criteria for determining locations where appropriate noise attenuation measures are warranted" and then conduct a noise survey along the entire 35-mile route.