Locus of Points Definition of an Ellipse, Hyperbola, Parabola, and Oval of Cassini

Given two points, and (the foci), an ellipse is the locus of points such that the sum of the distances from to and to is a constant. A hyperbola is the locus of points such that the absolute value of the difference between the distances from to and to is a constant. An oval of Cassini is the locus of points such that the product of the distances from to and to is a constant ( here). A parabola is the locus of points such that the distance from to a point (the focus) is equal to the distance from to a line (the directrix). This Demonstration illustrates those definitions by letting you move a point along the figure and watch the relevant distances change.