In mathematics, a parabola is a plane curve which is mirror-symmetrical and is approximately U-shaped. It fits several superficially different mathematical descriptions, which can all be proved to define exactly the same curves. One description of a parabola involves a point (the focus) and a line (the directrix).

A parabola is the locus of a point that is equidistant from a fixed point called the focus (F), and the fixed-line is called the Directrix (x + a = 0). Let us consider a point P(x, y) on the parabola, and using the formula PF = PM, we can find the equation of the parabola.

A parabola is a curve where any point is at an equal distance from: a fixed point (the focus), and; a fixed straight line (the directrix)

Sep 3, 2024 · Parabola is a symmetrical curve which is defined as the set of all points that are equidistant from a fixed point (called the focus) and a fixed straight line (called the directrix). The focus and directrix are two essential elements that determine the …

What is a parabola? A parabola is a particular type of geometrical curve which, algebraically, corresponds to a quadratic equation. In geometrical terms, the parabola corresponds to the edge of slice of an inverted cone; this slice is what is called the conic "section".

A parabola is the characteristic U-shaped curve of a quadratic equation. A parabola can be used to model many real-world phenomena. For example, when you shoot a basketball, the path of the ball creates a parabola. Below are two parabola graph examples, one in which the parabola opens upwards and one in which it opens downwards:

Apr 3, 2025 · parabola, open curve, a conic section produced by the intersection of a right circular cone and a plane parallel to an element of the cone—that is, the cone’s surface.

Parabolas are curves that contain points where their distances from the focus and their distances from the directrix will always be equal. The model below can help us visualize what this definition means. A parabola will contain three important elements: a focus, a directrix, and a vertex.

Feb 14, 2022 · Parabola: A parabola is all points in a plane that are the same distance from a fixed point and a fixed line. The fixed point is called the focus, and the fixed line is called the directrix of the parabola.

Mar 28, 2025 · Question 1: Write the standard equations of a parabola and a hyperbola and explain how their general forms differ. Question 2: Identify whether the equation x 2 =8y represents a parabola or a hyperbola. Justify your answer. Question 3: Sketch the graphs of the following equations and classify them as a parabola or hyperbola: y 2 = 16x