The study of Conic Curves has been each time less approached at High School and, in those few cases it is presented, it s possible to verify an improperly prioritized of equation memorizations. On the other hand, although the efficiency of the Origami is not often divulged at teaching mathematical subjects of greater complexity, there is a consistent axiomatic geometry behind this art of folding papers that makes it an a teaching tool able to explore, clearly, the properties and definitions of mathematical subjects. This study aims to join these two elements, conic curves and origami, in order to develop concepts from the first to building the second one. This way, it can make a historical and conceptual essay about the Conic Curves; describing the importance of the Origami and its use in Mathematics teaching; presenting the study of the seven possibilities for a single folding in Origami known as Huzita-Hatori s axioms in order to suggest the use of the folding in the study of ellipse, parable and hyperbole at High Schools all over the country. Divulging the Origami as an efficient and interesting resource in the teaching of the Conics and validate this research, a workshop was developed, applied, evaluated and improved in a small group of students of Degree in Mathematics and its results are exposed here.