Capella was the primary of the Capellan planetary system. This system had at least four planets, and one of them, Capella IV, was inhabited by a native species. This system was located in the Alpha Quadrant. Its location in the Milky Way Galaxy was depicted on a Federation star chart in 2293. (Star Trek VI: The Undiscovered Country, production art)
In 2267, the Federation and the Klingon Empire attempted to gain mining rights from the Capellans of Capella IV. The rare mineral topaline, vital to the life support systems of planetoid colonies, was in abundance there. The crew of the USS Enterprise secured the mining rights by treaty for the Federation. (TOS: "Friday's Child")
"The Explored Galaxy"
"The Explored Galaxy" was a map of charted space in the Alpha Quadrant. Capella 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".
Capella (Alpha Aurigae) was located in or near Federation space, in the Alpha Quadrant. This was a quadrinary star system. Capella A was a G class star with a magnitude of +3, which was ten times brighter than Sol. Capella B was a G class star. Capella C and Capella D were both M class stars. (pg. 36)