Conic Sections

Section 5.3 built every conic algebraically from the focus–directrix–eccentricity definition. There is also a purely geometric way to obtain the same four curves: slicing a double-napped cone (two identical cones joined tip-to-tip, sharing an axis) with a plane. Because a circle, ellipse, parabola or hyperbola can each be produced this way, they are collectively called conic sections, or simply conics — the name …