Fix two points, and (the foci), a distance apart. A Cassini oval (or Cassini ellipse) is a quartic curve traced by a point such that the product of the distances is a constant .

Let be the circle with center at the center of the oval and radius . Let be the right apex of the oval. A ray from at an angle to the line meets at the points and . Let be the circle with center and radius and let be the circle with center and radius . Let the point be one of the intersections of and . Then the product of the radii and is equal to the product , so is on the oval.