Parabola

A parabola is a plane curve whose points are equally distant from a fixed point, the focus, and a fixed line, the directrix. It is also the conic section formed by intersecting a cone with a plane parallel to one of its sides.

Focus (geometry): A fixed point used to define a conic section or specify a lens or mirror. Every point on a parabola is as far from this point as from the directrix.
Quadratic function: A function whose formula is a polynomial of degree two. Its graph is a parabola when the squared-variable coefficient is nonzero.
Parabolic reflector: A reflecting surface shaped as a paraboloid that concentrates parallel rays at a focus. Its cross-section is a parabola, which directs incoming parallel rays to one point.
Circle: The set of points in a plane at a fixed distance from one center. Unlike a parabola, a circle has a center and no directrix-based definition.
Directrix: A fixed line used with a focus to define a conic section. Its distance from each point on the parabola matches that point’s distance from the focus.
Vertex (geometry): The point at which a parabola changes direction along its axis of symmetry. It marks the parabola’s turning point and lies halfway between focus and directrix.
Parabolic antenna: An antenna using a parabolic reflector to transmit or receive electromagnetic waves. The reflector’s geometry focuses radio waves at its feed point.
Ellipse: A closed plane curve whose points have a constant sum of distances to two foci. An ellipse has eccentricity below one, whereas a parabola’s eccentricity is one.
Conic section: A curve formed by intersecting a plane with a double cone. A parabola is one of the four principal conic sections.
Axis of symmetry: A line that divides a figure into mirror-image halves. Each parabola is symmetric about the line through its focus and vertex.

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