The term HYPERBOLA PART is composed of two words, the first being 'HYPERBOLA' and the second being 'PART'. A HYPERBOLA is a type of conic section, which is a curve that is created by the intersection of a plane and a cone. The PART of the HYPERBOLA is the two branches that make up the curve, which are known as the directrix and the focus. The directrix is a line that is used to define the shape of the HYPERBOLA, while the focus is a point that is used to define the size of the HYPERBOLA. The ARC in this crossword solution refers to the ARC of the HYPERBOLA, which is the curved line that connects the two branches of the HYPERBOLA.