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Loading... 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). The focus does not lie on the ...
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- Definition
- On Paper
- Names
- Reflector
- Equations
- Measurements For A Parabolic Dish
A parabola is a curve where any point is at an equal distancefrom: 1. a fixed point (the focus), and 2. a fixed straight line (the directrix)
Get a piece of paper, draw a straight line on it, then make a big dot for the focus (not on the line!). Now play around with some measurements until you have another dot that is exactly the same distance from the focus and the straight line. Keep going until you have lots of little dots, then join the little dots and you will have a parabola! Just ...
Here are the important names: 1. the directrix and focus(explained above) 2. the axis of symmetry(goes through the focus, at right angles to the directrix) 3. the vertex(where the parabola makes its sharpest turn) is halfway between the focus and directrix.
And a parabola has this amazing property: Any ray parallel to the axis of symmetry gets reflected off the surface straight to the focus. And that explains why that dot is called the focus... ... because that's where all the rays get focused! So the parabola can be used for: 1. satellite dishes, 2. radar dishes, 3. concentrating the sun's rays to ma...
The simplest equation for a parabola is y = x2 Turned on its side it becomes y2= x (or y = √xfor just the top half) A little more generally: y2= 4ax where ais the distance from the origin to the focus (and also from the origin to directrix) The equations of parabolas in different orientations are as follows:
If you want to build a parabolic dish where the focus is 200 mm above the surface, what measurements do you need? To make it easy to build, let's have it pointing upwards, and so we choose the x2 = 4ayequation. And we want "a" to be 200, so the equation becomes: x2= 4ay = 4 × 200 × y = 800y Rearranging so we can calculate heights: y = x2/800 And he...
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 refers to an equation of a curve, such that a point on the curve is equidistant from a fixed point and a fixed line. Its general equation is of the form y^2 = 4ax (if it opens left/right) or of the form x^2 = 4ay (if it opens up/down)
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. As a plane curve, it may be defined as the path of a point moving so that its distance from a fixed line is equal to its distance from a fixed point.
- The Editors of Encyclopaedia Britannica
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.
www.storyofmathematics.com · parabolaParabola – Properties, Components, and Graph - The Story of ...
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.
