An implicit equation is a mathematical equation in which the relationship between the variables is not explicitly solved for one of the variables. In other words, it does not represent a function in the form of y = f(x), where you can isolate one variable (usually y) on one side of the equation and express it explicitly in terms of the other variable (x). Instead, in an implicit equation, both variables are typically interrelated within the equation, and you cannot easily isolate one variable. Therefore it is difficult to realize those Formulas with Blender Geometry Nodes.

Unlike the other sets of my Algebraic Surfaces, here the objects are build with the help of the new Volume Cube Node (+3.3). In the Documentation you find two detailed screenshots explaining the construction.

For performance reasons, the resolution is set to 200. If you want to have a smooth and clean object, you should increase the value to 800+ but you should decrease the value after rendering. Otherwise the Blend file gets big and laggy.

Please be aware that it is important to understand the idea of Geometry nodes.

(the glossy material is set1, the metal material is set2, the mixed material is for trial set)