Is it true the Carolina colony was owend and ruled by king of England?

No, the Carolina colony was not owned and ruled by the king of England. It was a proprietary colony, meaning that it was owned and controlled by a group of individuals, known as proprietors, who had received a charter from the king. The proprietors were granted the land and the right to establish a colony, and they had the authority to make laws, appoint officials, and collect taxes. The king did not have direct control over the Carolina colony, and he did not receive any revenue from it.