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Apollonius of Perga developed a systematic theory of conic sections. His surviving Conics studies the geometry of the ellipse, parabola and hyperbola, including their tangents and diameter relations.^[ref]

A single construction—cutting a cone by a plane—produces these different families of curves. Apollonius's work organizes their properties through geometric relations rather than modern Cartesian equations. Translating between those viewpoints helps explain why an equation such as $y^2=4ax$ describes a parabola without attributing coordinate notation to the ancient author.