A parabola is a type of conic section defined as the set of all points in a plane that are equidistant from a fixed point called the focus and a fixed line called the directrix. Parabolas have a characteristic U-shaped curve and can open either upwards, downwards, left, or right, depending on their orientation.
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A parabola is a plane curve whose points are equally distant from a focus and a directrix. In suitable coordinates it has equation , with . Its quadratic geometry can also describe a contour deformation through a saddle point.
For example, take a focus of a conic at and a directrix of a conic . Equality of squared Euclidean distances gives , hence . The point has distance to both the focus and the directrix. Its eccentricity of a conic is one. Unlike an ellipse, a parabola is unbounded and has only one matched focus-directrix description.