Question: In which villiage located in Schodack in Rensselaer County, New York was James Lawrence Hogeboom born?

Context paragraphs:
James L. Hogeboom: James Lawrence Hogeboom (August 25, 1766 Ghent, Columbia County, New York – December 23, 1839 Castleton-on-Hudson, Rensselaer County, New York) was an American merchant, lawyer and politician from New York.

Schodack Center, New York: Schodack Center is a hamlet in the town of Schodack, Rensselaer County, New York, United States.  Schodack Center is located at the junction of Interstate 90, U.S. Route 20, and U.S. Route 9.

East Greenbush Community Library: The East Greenbush Community Library serves a chartered special district, including the town of East Greenbush, New York and portions of the town of Schodack, New York under contract, bringing the total number of patrons to nearly 30,000.  The library is also a member of the Upper Hudson Library System, a resource-sharing consortium consisting of the 29 public libraries in Albany and Rensselaer Counties.  Located in southern Rensselaer County, New York, off Route 151 (Luther Road), the library shares a 39 acre tract of former farmland with the YMCA and Hawthorne Ridge, a multi-use senior housing complex.

Patroon Agent's House and Office: Patroon Agent's House and Office, also known as the Casparus Pruyn House and Office or Whish-Hull House and H. V. Rector office, is a historic home and office located on the Hudson River at Rensselaer in Rensselaer County, New York.  It was built and first occupied Nov. 29, 1839 and consists of a 2 ⁄ -story rectangular brick residence with an attached 1-story rectangular brick office in the Greek Revival style.  It was built by the Van Rensselaer family as a home and office for Casparus F. Pruyn, rent collection agent for William Van Rensselaer who had inherited the "East Manor" in 1839, consisting of Rensselaer County from his father Stephen.  Today, the Patroon Agent would be considered the Chief Operating Officer of a corporation; also, several other Patroon Agent Houses have been located in and around Albany over the 200+ years of the patroonship.

New York State Route 151: New York State Route 151 (NY 151) is an 8.23 mi state highway located in Rensselaer County, New York, in the United States.  Its western terminus is at an interchange with U.S. Route 9 (US 9) and US 20 in Rensselaer, and its eastern terminus is at a junction with NY 150 in Shivers Corners, a hamlet in the town of Schodack.  It also has an intersection with US 4 in East Greenbush.  NY 151 was assigned to most of its current alignment as part of the 1930 renumbering of state highways in New York.  In Rensselaer, NY 151 has been altered several times, with the most recent change coming in the late 1990s.  The current western terminus of NY 151 was once the western terminus of NY 43.

Egbert Ten Eyck: Egbert Ten Eyck (April 18, 1779 in Schodack, Rensselaer County, New York – April 11, 1844 in Watertown, Jefferson County, New York) was an American lawyer and politician from New York.

Schodack Landing Historic District: Schodack Landing Historic District is a national historic district located at Schodack Landing in Rensselaer County, New York.  It consists of 86 contributing buildings located in the hamlet of Schodack Landing.  The district includes a variety of buildings dated from the 18th through early 20th centuries.  They are mostly residential buildings, but include a post office, two churches, a nursing home, a tavern, and a store.  There are notable buildings in the Greek Revival and Italianate styles.

Castleton-on-Hudson, New York: Castleton-on-Hudson is a village located in the southwestern part of the town of Schodack in Rensselaer County, New York.  The population was 1,473 at the 2010 census.  The village is southeast of Albany, New York.

Schodack, New York: Schodack is a town in Rensselaer County, New York, United States.  The population was 12,794 at the 2010 census.  The town name is derived from the native word, Escotak.  The town is in the southwestern part of the county.  Schodack is southeast of Albany, New York.

Muitzes Kill Historic District: Muitzes Kill Historic District is a national historic district located at Schodack in Rensselaer County, New York.  It consists of 23 contributing buildings located in the hamlet of Muitzes Kill, or Muitzeskill ("kill" is derived from archaic Dutch for "creek").  The district is one of two in the town of Schodack, the other being Schodack Landing Historic District just two miles west where Muitzeskill Road meets the Hudson River.

Supporting paragraphs: James L. Hogeboom Castleton-on-Hudson, New York
Answer: Castleton-on-Hudson