Apollonius of Perga
The greatest progress in the study of conics by the ancient Greeks is due to Apollonius of Perga (died c.190 BC) ), whose eight volume Conic Sections summarized the existing knowledge at the time and greatly extended it. Apollonius's major innovation was to characterize a conic using properties within the plane and intrinsic to the curve; this greatly simplified analysis. With this tool, it was now possible to show that any plane cutting the cone, regardless of its angle, will produce a conic according to the earlier definition, leading to the definition commonly used today.
Pappus of Alexandria (died c. 350 CE) is credited with discovering importance of the concept of a focus of a conic, and the discovery of the related concept of a directrix.
Read more about this topic: Conic Section, History