A plane curve having two branches, formed by the intersection of a plane with both halves of a right circular cone at an angle parallel to the axis of the cone. It is the locus of points for which the difference of the distances from two given points is a constant. (hi:-purr'bə-lə) The plural form can be either hyperbolas or hyperbolae.Related links: A diagram of conic sections including a circle, an ellipse, a parabola, and a hyperbola. Also see arc, cone, cylinder, ellipse, hyperbole, parabola, and sphere.