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.