Focus (geometry)

A focus is a fixed point used in geometric definitions of curves. Ellipses and hyperbolas use two foci, while a parabola uses one focus and a directrix.

Euclidean distance: The straight-line distance between two points in Euclidean space. Distances from a focus determine which points belong to a conic.
Ellipse: A closed conic curve whose points have a constant sum of distances from two foci. Its two foci jointly determine the defining constant-sum condition.
Reflecting telescope: A telescope that uses mirrors to collect and focus light. Parabolic mirrors direct incoming parallel light toward a focus.
Center (geometry): A point serving as the midpoint or symmetry center of a geometric figure. An ellipse has a center between its foci, but the center does not define its distance condition.
Locus (mathematics): A set of points satisfying a specified condition. Conic sections are loci defined by distances to foci and other fixed features.
Parabola: A conic curve whose points are equally distant from a fixed focus and directrix. Its single focus works with a directrix rather than a second focus.
Whispering gallery: An architectural space in which sound can travel unusually clearly between distant points along a curved wall. An elliptical plan can carry sound from one focus to the other.
Vertex (geometry): A point where two or more lines, edges, or curve branches meet, or an extremal point of a curve. A conic's vertices mark extremes, while its foci govern distance relations.
Conic section: A curve formed by intersecting a cone with a plane, or described by a quadratic equation. Foci are defining features of several familiar conic sections.
Hyperbola: A conic curve whose points have a constant absolute difference of distances from two foci. Its two foci define a constant-difference condition, unlike an ellipse.

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