Elaysian homeworld
The Elaysian homeworld was an inhabited planet. 

The planet had low surface gravity. This was the homeworld of the humanoid Elaysians and the garlanic tree. Only a handful of Elaysians ever left the homeworld, one of whom was Melora Pazlar. ()

Appendices

Background information 
At StarTrek.com, the planet was named Elaysia and was classified as a M-class planet. 

According to the reference book Star Trek: Star Charts ("United Federation of Planets I"), Elaysia was listed as Federation member in 2378.

Apocrypha 
The Pocket TNG s Gemworld, Book One and Gemworld, Book Two stated that the Elaysian homeworld was Gemworld, a planet considered artificial by some, due to the fact that it should have been extinct long ago, but was kept alive with a "shell" force field and shield setup that also collected different chemicals and substances to convert into energy to feed the Crystal that was now all that was left of their planet. It concluded that, whereas the Frills were native to Gemworld, the planet had been populated with Elaysian, Alpusta, Gendelli, and Yiltern, who were all transplanted from a different dimension by the , oldest of the planet's inhabitants.

External link 
 

de:Heimatwelt der Elaysianer
ja:エレージアンの母星
nl:Elaysian thuiswereld
Unnamed planets
Homeworlds