Alpha Majoris I was the homeworld of the mellitus. It was the first planet of the Alpha Majoris planetary system. This system was located in the Alpha Quadrant. (TOS: "Wolf in the Fold"; Star Trek VI: The Undiscovered Country, production art)
"The Explored Galaxy" was a map of charted space in the Alpha Quadrant. Alpha Majoris was located between the Tholian Assembly and Romulus. Both locations were identified in DS9: "The Search, Part II", "Call to Arms" as being located in this quadrant. The chart, first seen chronologically in Star Trek VI: The Undiscovered Country, was also seen in several Star Trek: The Next Generation and Star Trek: Deep Space Nine episodes set in the 24th century, from the year 2364 to 2370. These were TNG: "Conspiracy", "The Measure Of A Man", "The Emissary", "The Mind's Eye", "The Game", and DS9: "In the Hands of the Prophets", "Cardassians".