means A hyperbola is the open, two-branched curve you get when a plane slices through both halves of a cone, defined by every point whose distances from two fixed foci differ by a constant.

from From Greek "hyperbolē," meaning "a throwing beyond" or "excess" — from "hyper" (over, beyond) plus "ballein" (to throw). The ancient Greek geometer Apollonius of Perga named the three conic sections by how the cutting plane's angle compared to the cone's side: the "ellipse" fell short, the "parabola" ran alongside, and the "hyperbola" overshot — its plane tilted so steeply it sliced through both cones. The very same root gives us "hyperbole," that rhetorical overshooting into exaggeration; the curve and the figure of speech are true cousins, both born from the Greek love of throwing too far.