Final answer:
Eukaryotes are found (A) only within the domain Eukarya, one of the three domains of life, which also include the prokaryotic domains Bacteria and Archaea.
Step-by-step explanation:
In the three-domain system, eukaryotes are represented only within the domain Eukarya. This domain is unique in that it houses organisms whose cells contain a nucleus, where their genetic material is enclosed. Organisms such as plants, animals, fungi, and protists all fall under this domain.
On the other hand, prokaryotes, which do not have a nucleus, are classified into the other two domains: Bacteria and Archaea. Despite Archaea often being extremophiles and Bacteria being omnipresent in milder environments, neither contain eukaryotic organisms. Therefore, the correct answer to the student's question would be only within the domain Eukarya, option A.