What does parabola mean?
A parabola is an open, symmetrical plane curve that forms one type of conic section. Its defining property is geometric: every point on the curve is the same distance from a fixed point, called the focus, and a fixed straight line, called the directrix. In algebra, the familiar graph of y = x² is a parabola, with rotations and translations producing many other orientations and positions. The word is chiefly used in mathematics, but it also describes idealized trajectories: for example, a ball's path can be modelled approximately as a parabola when air resistance and Earth's curvature are neglected. Such descriptions are useful because a parabola has predictable behavior, including a single vertex and a mathematically regular change in direction. Outside technical contexts, the term can suggest a rapid rise and fall, although that figurative use is less precise than the geometrical definition.
nounA parabola is a conic section consisting of all the points in a plane that are equidistant from a fixed point, called the focus, and a fixed line, called the directrix.
- A conic section formed by the set of points in a plane that are equidistant from a fixed point and a fixed line.
"The graph of y = x² is a parabola whose vertex is at the origin."
"The graph of y = x² is a parabola whose vertex is at the origin."
"Ignoring air resistance, the ball follows an approximately parabolic path."
The standard plural adds -s; parabolae is occasionally encountered in more formal or traditional mathematical writing but is not the usual modern plural.
"Several parabolas can be plotted on the same coordinate grid."
Every point on a parabola is equally distant from a fixed point and a fixed line—a remarkably elegant way to draw a curve with only two rules.
Reviewed by Deb Chak, Editor. AI-assisted content curated by RJS Tech Solutions LLP.
Etymology of parabola
The English noun comes through Latin from Greek parabolē, meaning “comparison” or “a placing side by side.” Greek paraballein combines para-, meaning “beside,” with ballein, meaning “to throw.” The mathematical sense developed through early modern European studies of conic sections, while parable is a cognate that retains a separate story-related meaning.
Related word forms
How parabola is actually used
Parabola is primarily a technical mathematical noun. In physics, a trajectory is described as parabolic only as an idealization, normally neglecting air resistance and the curvature of Earth.
Easily confused with parabola
A parabola is a geometric curve, whereas a parable is a short story that conveys a moral or lesson.