circle tangent

Given two concentric circles, with radius r₀ and r₁ respectively, a curve tangent to both of them can be imagined. I named the curve the circle tangent.
The constant a is equal to r₁/r₀ - 1.

The degree of the corresponding Cartesian equation is equal to 2b + 2.
For large b, the curve has a long tangent to one of the circles, the inner for positive values for parameter a, the outer for negative values for the parameter a.

It is possible that the Saint-Hilaire skating rink curve belongs to this family.