A hyperbola is a type of smooth curve that lies in a plane and resembles two infinite bows or branches that are mirror images of each other. It is one of four conic sections formed by the intersection of a plane and a cone, with the others being a parabola, ellipse, and circle. A hyperbola is formed when the angle between the intersecting plane and the cone's axis is less than the angle between a line on the cone's surface and its axis, or if the plane is parallel to the axis.