What kind shape?

A line segment with a string tied in the middle (like _|_). Now, tie a pen at the other end of string and draw a closed curve. When drawing the curve, the string is tight and it moves on the line smoothly. What is the shape of the curve? A more general question is changing the line to be a loose string. In this case if the string in the middle has lentgh 0, the curve would be an oval.