Elements of the parabola in the three-dimensional space and applications in teaching through a project based on reflection of light

This work, structured in two main parts, is devoted to the parabola topic. In the first, the elements of a parabola are reviewed by linking the definition of intersection of a plane and a cone with a locus of the plane. The necessary transformations for the calculation of the elements as a curve in space are pointed out as well as historical notes and properties of light are included. In the second part, the applications in teaching at a high school level or university courses are explained. A project based on the reflection of light is proposed that seeks to connect various subjects in line with the new educational paradigm of development of key competencies, joining different fields of knowledge. For university courses, applications of linear algebra are obtained in the establishment of relationships between analytical geometry in the rotation and translation of planes, and the dihedral system that is taught in technical drawing subjects. As a conclusion, it is obtained that the teaching of the parabola from different approaches allows a complete learning of diverse fields of knowledge, even of different topics of mathematics, an essential factor in the development of thought at any educational level.