Step 1: Understanding the Question
This is a history question asking to identify the king who was the patron of the poet Ashvaghosha, the author of the Buddhacharita.
(Note: The question has a grammatical error; it should be "...live?" or "...lived?").
Step 2: Recalling Historical Facts
Ashvaghosha was a prominent Buddhist philosopher, poet, and dramatist from India.
He is most famous for his epic poem "Buddhacharita" (The Acts of the Buddha).
Historical accounts place him as a contemporary and spiritual advisor to the Kushan emperor Kanishka the Great, who reigned in the 2nd century CE.
Kanishka was a great patron of Buddhism and convened the Fourth Buddhist Council, in which Ashvaghosha is believed to have played a significant role.
Step 3: Evaluating the Options
(A) Kanishka: This is historically correct. Ashvaghosha was a key figure in the court of the Kushan king Kanishka.
(B) Asoka: He was a Mauryan emperor who lived several centuries before Kanishka and Ashvaghosha.
(C) Krishnadevaraya: He was the emperor of the Vijayanagara Empire in the 16th century, much later in history.
(D) Pushyamithra: This refers to Pushyamitra Shunga, founder of the Shunga Empire, who lived after the Mauryas but before the Kushans.
Step 4: Final Answer
Historical evidence strongly associates the poet Ashvaghosha with the court of Kanishka. Therefore, option (A) is the correct answer.