The location of Gamma Hydra on the tactical situation monitor
Quadrant 448 was, in 2267, the location of a rogue comet that had recently passed through the Gamma Hydra system. This quadrant was located in the Gamma Hydra sector, which was a region of space in the Alpha Quadrant. (TOS: "The Deadly Years"; TNG: "Yesterday's Enterprise", display graphic)
In the tactical situation monitor, several of the locations on this monitor, such as Alpha Carinae and Rigel, were identified by "The Explored Galaxy" star chart as being in the Alpha Quadrant.
This use of the term quadrant occurred before the current standardization of the quadrant/sector model of stellar cartography.