1. Normal and Tangent to a Cassini Oval

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 .

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