Nope-don't have to feed them. They have the single celled organisms inside them that help feed them.....zooxanthellae. They provide added nutrients to help feed the corals and to keep them healthy. A strong light is needed to keep producing and keep these creatures alive. Sometimes food may pass by a coral and a "arm" might reach out and grab it and put it in it's mouth. But those types of corals don't need to be fed they feed themselves.
peace
doug