The implicit function theorem describes conditions under which an equation formula_2 can be "solved implicitly" for "x" and/or "y" – that is, under which one can validly write formula_12 or formula_4. This theorem is the key for the computation of essential geometric features of the curve: tangents, normals, and curvature. In practice implicit curves have an essential drawback: their visualization is difficult. But there are computer programs enabling one to display an implicit curve. Special properties of implicit curves make them essential tools in geometry and computer graphics.