How is a parabola defined?

A parabola is defined as a specific type of curve on a plane that can be described mathematically by a quadratic equation. It is the set of all points in a plane that are equidistant from a fixed point known as the focus and a fixed line known as the directrix. This geometric definition emphasizes its nature as a smoothly curved, continuous line rather than having straight segments or distinct endpoints.

The nature of a parabola allows it to open either upwards or downwards (or sideways depending on its orientation), forming a "U"-shaped figure. This characteristic distinguishes it from other types of curves, such as circles or closed curves, which do not have the same properties of symmetry around a single axis and do not consist of points that follow the relationship defined by the focus and directrix. Therefore, describing a parabola as a curved line on a plane captures its essential properties accurately, making this the correct choice in the context of geometric definitions.