Bivariate cubic equations define curves in the coordinate plane. Unlike simple functions, these equations involve both x and y variables raised to various powers, with the total degree being three. The example shown is the folium of Descartes, defined by x cubed plus y cubed minus three x y equals zero. These curves often have interesting geometric properties and cannot be expressed as simple functions.
The general form of a bivariate cubic equation contains ten coefficients, representing all possible terms up to degree three. Famous examples include the folium of Descartes, which creates a loop-like curve, and the cissoid of Diocles, used historically to solve the problem of doubling the cube. Each curve type has distinct geometric characteristics and mathematical applications.