the barycenter of the Moon and the Earth, this barycenter being within the Earth itself, while the Earth (more precisely, its center) moves in an ellipse with one focus at that same barycenter within the Earth. The barycenter is about three-quarters of the distance from Earth's center to its surface. Moreover, the Pluto-Charon system moves in an ellipse around its barycenter with the Sun, as does the Earth-Moon system (and every other planet-moon system or moonless planet in the solar system). In both cases the barycenter is well within the body of the Sun. Two binary stars also move in ellipses sharing a focus at their barycenter; for an animation, see here. Cartesian and Cassini ovals A Cartesian oval is the set of points for each of which the weighted sum of the distances to two given foci is constant. If the weights are equal, the special case of an ellipse results. A Cassini oval is the set of points for each of which the product of the distances to two given foci is constant. Generalizations An n-ellipse is the set of points all having the same sum of distances to n foci (the n = 2 case being the conventional ellipse). The concept of a focus can be generalized to arbitrary algebraic curves. Let C be a curve of class m and let I and J denote the circular points at infinity. Draw the m tangents to C through each of I and J. There are two sets of m lines which will have m2 points of intersection, with exceptions in some cases due to singularities, etc. These points of intersection are the defined to be the foci of C. In other words, a point P is a focus if both PI and PJ are tangent to C. When C is a real curve, only the intersections of conjugate pairs are real, so there are m in a real foci and m2 − m imaginary foci. When C is a conic, the real foci defined this way are exactly the foci which can be used in the geometric construction of C. Confocal curves Let P1, P2, ..., Pm be given as foci of a curve C of class m. Let P be the product of the tangential equations of these points and Q the product of the tangential equations of the circular points at infinity. Then all the lines