"Yes, the cat is there."
Translation:Так, кіт там.
No, we don't have a concept of articles so we don't differentiate between "the cat" and "a cat" at all, therefore, кіт can be translated to either depending on the context.
When we want to achieve a specification obtained by using "the" in English we just literally say "this cat" (цей кіт) or "that cat" (той кіт), while "a cat" will definitely just be кіт
If you really need to specify an object, you can use the equivalent of "this/that/yon" + the noun in Slavic languages. Besides that option, in the other cases you should rely on your intuition.
PS Some Slavic languages (Bulgaro-Macedonian and some dialects of Slovenian) have "proper" definite articles, which are enclitic post-positions formed by "this/that/yon".