The conics are very beautiful mathematical objects, among these figures, perhaps the best known is the circle or the ellipse, but there are two others, the parabola and the hyperbola. All these figures are named after the fact that when cutting a double cone with a plane, these objects are formed.

The object of the present text is to study the conics from the perspective given by the Cartesian plane, allowing to represent the points as pairs of numbers, and in this way, expressing the conics as equations of the second degree in two letters.

That said, in the first part we study the ring of polynomials, in general, and their arithmetic properties. The factorization of polynomials and its application in solving equations is studied. Systems of equations are also studied.

In the second part, the conics are studied, from their definition as objects in the plane, to their equations.

The topics we are dealing with correspond to a course in algebra and analytical geometry but focused on the study of conics.