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ellipse vs. hyperbola

ellipse

[ ih-lips ]
noun
  1. a plane curve such that the sums of the distances of each point in its periphery from two fixed points, the foci, are equal. It is a conic section formed by the intersection of a right circular cone by a plane that cuts the axis and the surface of the cone. Typical equation: (x2/a2) + (y2/b2) = 1. If a = b the ellipse is a circle.

hyperbola

[ hahy-pur-buh-luh ]
noun
  1. the set of points in a plane whose distances to two fixed points in the plane have a constant difference; a curve consisting of two distinct and similar branches, formed by the intersection of a plane with a right circular cone when the plane makes a greater angle with the base than does the generator of the cone. Equation:x2/a2 − y2/b2 = ±1.