Final answer:
Henry Hudson was the explorer who explored the Hudson Bay area looking for a passage to the Far East. He was hired by Dutch merchants in 1609 but did not find the Northwest Passage. Additionally, Pedro Cabral was the first to claim Brazil for Portugal, not Columbus, Magellan, or Cartier.
Step-by-step explanation:
The explorer who ventured into the Hudson Bay area in search of a passage to the Far East was Henry Hudson. In 1609, he was hired by Dutch merchants to find the elusive Northwest Passage. Although Hudson discovered a deep-water port and the river that would later bear his name, he did not find the passage to Asia. Neither the Delaware Bay nor the Hudson River turned out to be the Northwest Passage, but they were significant in establishing lucrative avenues for fur trading and farming, which paved the way for Dutch colonization efforts in the region.
Regarding Columbus, although he made four voyages to the Caribbean between 1492 and 1504, he was not the explorer who reached the Hudson Bay area nor did he find a route to Asia as he had intended. Nevertheless, Columbus's voyages were significant for being among the earliest European expeditions that led to permanent contact with the Americas.
As for the question about the first explorer to reach Brazil and claim it for the throne of Portugal, the correct answer is Pedro Cabral. This claim was not made by Christopher Columbus, Ferdinand Magellan, or Jacques Cartier, as they were involved in different expeditions contributing to the Age of Discovery in other areas.