Parabola

A parabola is a plane curve whose points are equally distant from a focus and a directrix. In suitable coordinates it has equation

y = a x^{2}

, with

a \neq = 0

. Its quadratic geometry can also describe a contour deformation through a saddle point.

For example, take a focus of a conic at

(1, 0)

and a directrix of a conic

x = - 1

. Equality of squared Euclidean distances gives

(x - 1)^{2} + y^{2} = (x + 1)^{2}

, hence

y^{2} = 4 x

. The point

(1, 2)

has distance

2

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.

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- Vertex of a parabola Parabola

Vertex of a parabola ( $(h, k)$ )

 0  0

For a parabola described by the function graph

y = a (x - h)^{2} + k

, with nonzero

a

in the real numbers, its vertex of a parabola is the point

(h, k)

. This point gives its minimum or maximum value of

y

in these coordinates.

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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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Parabola

Vertex of a parabola ( $(h, k)$ )

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Parabola

Vertex of a parabola ((h,k))

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