# 1. Constructing a Point on a Cassini Oval

1. Constructing a Point on a Cassini Oval

This Demonstration shows a ruler and compass construction of a point on a Cassini oval.

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 .

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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.

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