Very bright light in night sky leaving at incredible speed from an apparent hovering position

My parents related this to me when I was 8 or 9 years old.  They were driving northbound on US-1 in the early AM in the dark before sunrise in the vicinity of what is now known as Pinecrest. In the 1960's, it was a semi-rural area.  My dad spotted what he thought was an aircraft to the north of their position.  He said it was a very bright white light that stayed in one position.  He assumed that it was an airplane with its landing lights on heading for Miami International Airport. When it didn't appear to turn he was afraid that it may be making an emergency landing on the highway! As my mom and dad became concerned, the object shot away to the west at incredible speed. My dad said that it left like a bullet shot from a gun, leaving only a line in the sky. This was no airplane.
Date is approximate.  PD