A plane curve is a two-dimensional geometric shape that is defined by a mathematical equation. The three most common types of plane curves are CONIC, PARABOLA, and ELLIPSE. A CONIC is a curve that is created by the intersection of a plane and a cone. A PARABOLA is a U-shaped curve that is created by the intersection of a plane and a double cone. An ELLIPSE is an oval-shaped curve that is created by the intersection of a plane and a cone.