An algebraic curve or plane algebraic curve is the set of points on the Euclidean plane whose coordinates are zeros of some polynomial in two variables.
An algebraic curve in the Euclidean plane is the set of the points whose coordinates are the solutions of a bivariate polynomial equation p(x, y) = 0. This equation is often called the implicit equation of the curve, by opposition to the curves that are the graph of a function defining explicitly y as a function of x.
Given a curve given by such an implicit equation, the first problems that occur is to determine the shape of the curve and to draw it. These problems are not as easy to solve as in the case of the graph of a function, for which y may easily be computed for various values of x. The fact that the defining equation is a polynomial implies that the curve has some structural properties that may help to solve these problems.