Questions & Answers about Koppen er populær i hjemmet.
In Danish, the is often built into the noun itself instead of being a separate word.
- kop = cup
- koppen = the cup
- hjem = home
- hjemmet = the home
So in Koppen er populær i hjemmet, both koppen and hjemmet are definite forms.
A useful extra point: when there is an adjective directly before the noun, Danish often uses both a separate word and the ending:
- den populære kop = the popular cup
But in your sentence, populær comes after er, so you just get koppen.