This Demonstration shows how to construct the normal and tangent to a Cassini oval at a point .

A Cassini oval is the locus of points such that , where and . If the foci and , then

, .

For the normal vector at a point on the oval,

,

where is the unit vector in the direction of .

Thus the normal to the Cassini oval at is a diagonal of the parallelogram obtained by extending the vector by and extending by , where . Then the tangent is the perpendicular to at .