WOLFRAM|DEMONSTRATIONS PROJECT

Cassini Ovals

​
vary parameter b/a
1
special cases
two loops
lemniscate
dog bone
single oval
This Demonstration shows the family of Cassini ovals (or Cassini ellipses). These curves are traced by a point such that the product of its distances from two fixed points a distance
2a
​
apart is a constant
2
b
.
The shape depends on
b/a
. If
a<b
, the curve is a single loop. The case
a=b
produces a lemniscate. If
a>b
, then the curve consists of two loops.