left hook

When throwing the left hook on the outside am i supposed to keep my elbow down as i know that when throwing a hook on the inside you got to get the elbow up so the forearm is parallel to the floor but does that mean that the further out i throw it the lower my elbow should be?? with the forearm sort of at a 45 degree angle?? I notice most people throw hooks with the elbow down is that just because they are throwing them at longer range as opposed the the short elbow up palm down style that beginers get taught.... ???