Final answer:
Vermont is the state with Burlington as its largest city; it is situated on Lake Champlain near the Canadian border.
Step-by-step explanation:
The state whose largest city is Burlington, located on the eastern shore of Lake Champlain and 45 miles from the Canadian border, is Vermont.
Burlington is well known as a cultural hub and is the most populous city in Vermont. In contrast to this information, New York City is mentioned as the largest city in the United States and has its own distinct growth history, which includes transportation advantages like the Hudson River and the Erie Canal.