Hyperbola Evolute

The Evolute of a Rectangular Hyperbola is the Lamé Curve

$$(ax)^{2/3} - (by)^{2/3} = (a+b)^{2/3}.$$

From a point between the two branches of the Evolute, two Normals can be drawn to the Hyperbola. However, from a point beyond the Evolute, four Normals can be drawn.