Not only can they utilize the photosynthetic products of their algal symbionts but they can also feed directly on plankton, bacteria, detritus and fish feces. Other zooxanthellae bearing organisms include some sponges and Tridacna spp. As mentioned above, most corals contain symbiotic algae in their tissues which can supply some of their nutritive needs. I say some because the degree to which zooxanthellae contribute to a coral's nutrition has been the subject of much research over the past 40 years. It seems that the amount varies between species.
Corals feed in a variety of ways.
The problem comes when deciding when and how much to feed. In my own personal opinion many coral species do not need direct feeding. Many get more than enough from natural sources in the tank. Every time you feed your fish, particles of food and nutrients are added to the water. The presence of live rock and their associated algae and bacteria produce copious amounts of nutrients, vitamins and other products.