and other level lines of f(x,y) = ((x-1)^2+y^2)*((x+1)^2+y^2)-1

The level curves of the function

f(x,y) = ((x-1)^2+y^2)*((x+1)^2+y^2)-1

can be computed from the ODE:

c'(t) = Rot90(grad f)(c(t))

where grad f vanishes only at [x,y] = [0,0].

The Cassini Eight has a double point singularity

at the origin.

The product-form of the function f shows that on

each level line the product of the distances from

[1,0] and [-1,0] is constant.

f(x,y) = ((x-1)^2+y^2)*((x+1)^2+y^2)-1

can be computed from the ODE:

c'(t) = Rot90(grad f)(c(t))

where grad f vanishes only at [x,y] = [0,0].

The Cassini Eight has a double point singularity

at the origin.

The product-form of the function f shows that on

each level line the product of the distances from

[1,0] and [-1,0] is constant.