Lemniscate of Bernoulli is Special Case of Ovals of Cassini/Cartesian Proof

Proof
The ovals of Cassini can be defined by a Cartesian equation as follows:

The lemniscate of Bernoulli can be defined by a Cartesian equation as follows:

Setting $b = a$:

It follows that the lemniscate of Bernoulli is an oval of Cassini where $b = a$.