Lemniscate of Bernoulli

The lemniscate of Bernoulli came up in a post a few days ago. This shape is a special case of a Cassini oval:

((x + a)^2 + y^2) ((x - a)^2 + y^2) = a⁴.

Here's another way to arrive at the lemniscate. Draw a hyperbola (blue in the figure below), then draw circles centered at points on the hyperbola and passing through the center of the hyperbola. The figure-eight that is traced out in the middle is a lemniscate.

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