In mathematics, an ellipse is a plane curve surrounding two focal points, such that for all points on the curve, the sum of the two distances to the focal points is a constant. As such, it generalizes a circle, which is the special type of ellipse in which the two focal points are the same. The elongation of an ellipse is measured by its eccentricity formula_1, a number ranging from formula_2 (the limiting case of a circle) to formula_3 (the limiting case of infinite elongation, no longer an ellipse but a parabola).