Question: Ballston Lake is located northeast of which New York hamlet?

Context paragraphs:
Forest Park (Ballston Lake, New York): Forest Park was a trolley park in the town of Ballston, New York.  The park was built by the Schenectady Railway Company, owned by General Electric.  It consisted of 144 acres located at the south end of Ballston Lake along the company's Schenectady to Saratoga Springs trolley line, and was serviced by a dedicated stop.  It opened in 1904 and closed in 1927.  By 1908 the park was said to have attracted between 75,000 and 100,000 visitors every season.

Enable Software, Inc.: Enable Software was a privately held software development company located in Ballston Lake, New York.  Their flagship product, called "Enable" was an integrated office suite for DOS-based IBM PC compatible computers.  Enable was founded in 1984 by Ron Quake and Bob Hamilton.

New York State Route 146A: New York State Route 146A (NY 146A) is a state highway in New York State.  It begins at NY 146 in Clifton Park and ends at NY 50 in Ballston Lake.  It is located entirely within Saratoga County.  Route 146A is the last existing spur of NY 146 in Saratoga and Schenectady counties.

Burnt Hills, New York: Burnt Hills is a hamlet within the town of Ballston, in Saratoga County, New York, United States.  Its ZIP code is 12027.

Shenendehowa Central School District: The Shenendehowa Central School District, often shortened to Shen, is a public school district located in New York's Capital Region.  The district's 232 acre main campus is located off NY 146 in Clifton Park, and is home to eight of the districts 12 schools, in five buildings.  The remaining four schools are so called "neighborhood elementary schools" and are located throughout the district in three buildings.  The district serves approximately 9,800 students in grades K-12 from throughout its 86 sqmi territory which includes the towns of Clifton Park, Halfmoon, Ballston Lake, Round Lake, Malta and parts of Waterford, Rexford, Mechanicville and Stillwater.  Shenendehowa is the largest School District in Saratoga County, and the largest in student population in the Suburban Council, an interscholastic athletic consortium of 11 area school districts.

Ballston Lake: Ballston Lake is a lake that is located northeast of Burnt Hills, New York.  Fish species present in the lake are northern pike, smallmouth bass, largemouth bass, yellow perch, northern pike, carp, pumpkinseed sunfish, and brown bullhead.  A monster known as big Tim is rumored to live in the caves at the bottom of the lake.  There is a private boat launch that can be accessed by paying fee, located on the north shore off Outlet Road.

York Hamlet, New York: York Hamlet is a hamlet and census-designated place in Livingston County, New York, United States.  Its population was 544 as of the 2010 census.  New York State Route 36 passes through the community.

New York State Baseball Hall of Fame: The New York State Baseball Hall of Fame is a hall of fame based in Ballston Lake, New York in the United States, founded in 2010 as an achievement award for baseball in the state.

Ballston Creek: Ballston Creek, also called Shenantaha Creek from the Iroquios name for Ballston Lake ("deep water"), is a stream in Saratoga County, New York.  It originates at the north end of Ballston Lake and runs approximately six miles (9.7 km) through the towns of Ballston and Malta, descending 100 feet before exiting into Round Lake.

New York State Route 339: New York State Route 339 (NY 339) was a state highway located within the town of Ballston in Saratoga County, New York, in the United States.  The road's western terminus was at an intersection with NY 50 and County Route 58 (CR 58) in the hamlet of Burnt Hills.  Its eastern terminus was at a junction with NY 146A near the hamlet of Ballston Lake.

Supporting paragraphs: Ballston Lake Burnt Hills, New York
Answer: Burnt Hills