The location of Gamma Hydra on the tactical situation monitor
Gamma Hydra II was an uninhabited planet. It was the second planet in the Gamma Hydra planetary system. This system was located in the Gamma Hydra sector, which was a region of space in the Alpha Quadrant.
When crewmembers of the USS Enterprise, including Captain Kirk were afflicted by radiation on Gamma Hydra IV, causing them to age rapidly, Kirk several times mistakenly stated that the Enterprise orbited Gamma Hydra II because of the decreased mental capabilities due to his "old age". (TOS: "The Deadly Years")
The tactical situation map depicted an area of space in the Alpha Quadrant. The locations Eminiar, Janus VI, Rigel, Andor, Babel, and Delta Vega were identified on "The Explored Galaxy" wall chart as being located in this quadrant.
According to the Star Trek: Star Charts (pgs. 56, 66), Gamma Hydra II was located in or near Federation space. In 2378, the Gamma Hydra system was a destination on the major space lanes.