Which Greek mathematician is known for developing the concept of conic sections?

Apollonius of Perga was the Greek mathematician best known for developing the theory of conic sections.

His major work, Conics, was an eight-book treatment of curves formed by slicing a cone with a plane. Apollonius built on earlier investigations by mathematicians including Euclid and Archimedes, but greatly extended the subject and brought it to a level that influenced geometry for centuries. He gave the curves the names ellipse, parabola, and hyperbola that remain standard today.

Apollonius worked with conics through rigorous geometric constructions rather than algebraic equations or coordinate graphs. That means he did not create modern analytic geometry, which emerged much later with René Descartes and Pierre de Fermat. The common mix-up is to credit Apollonius with discovering every conic section; earlier Greek mathematicians had studied some of them. His distinctive achievement was organizing, naming, and substantially advancing their general theory.