A plane curve in mathematics that is approximately u-shaped

Today's crossword puzzle clue is a general knowledge one: A plane curve in mathematics that is approximately U-shaped. We will try to find the right answer to this particular crossword clue. Here are the possible solutions for "A plane curve in mathematics that is approximately U-shaped" clue.

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 directrix. The parabola is the locus of points in that plane that are equidistant from the directrix and the focus. Another description of a parabola is as a conic section , created from the intersection of a right circular conical surface and a plane parallel to another plane that is tangential to the conical surface. The line perpendicular to the directrix and passing through the focus that is, the line that splits the parabola through the middle is called the "axis of symmetry".

A plane curve in mathematics that is approximately u-shaped

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It can easily be shown that the parallelogram has twice the area of the triangle, so Archimedes' proof also proves the theorem with the parallelogram. The parabolic orbit is the degenerate intermediate case between those two types of ideal orbit. Aircraft used to create a weightless state for purposes of experimentation, such as NASA 's " Vomit Comet ", a plane curve in mathematics that is approximately u-shaped, follow a vertically parabolic trajectory for brief periods in order to trace the course of an object in free fallwhich produces the same effect as zero gravity for most purposes.

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Online Math Solver. In geometry, a parabola is a two-dimensional, mirror symmetrical curve which is approximately U-shaped. It fits any of several superficially different mathematical descriptions which can all be proved to define curves of exactly the same shape. One description of a parabola involves a point the focus and a line the directrix. The focus does not lie on the directrix. The vertex is the point where the parabola intersects its axis of symmetry. The term "parabola" is derived from the Latin word parabolus, which means "to throw" or "to place side by side. A parabola can open either upwards or downwards. The line that bisects a parabola at its vertex is called its "axis of symmetry. Any ray perpendicular to the axis of symmetry and passing through the focus will reflect off the surface of the parabola and appear to originate from the vertex.

A plane curve in mathematics that is approximately u-shaped

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 directrix. The parabola is the locus of points in that plane that are equidistant from the directrix and the focus. Another description of a parabola is as a conic section , created from the intersection of a right circular conical surface and a plane parallel to another plane that is tangential to the conical surface.

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The focus is F, the vertex is A the origin , and the line FA is the axis of symmetry. See animated diagram [8] and pedal curve. P is an arbitrary point on the parabola. Today, paraboloid reflectors can be commonly observed throughout much of the world in microwave and satellite-dish receiving and transmitting antennas. University of Texas at Austin. At higher speeds, such as in ballistics, the shape is highly distorted and does not resemble a parabola. The focal length can be determined by a suitable parameter transformation which does not change the geometric shape of the parabola. Remark 2: The 2-points—2-tangents property should not be confused with the following property of a parabola, which also deals with 2 points and 2 tangents, but is not related to Pascal's theorem. In nature, approximations of parabolas and paraboloids are found in many diverse situations. The name "parabola" is due to Apollonius , who discovered many properties of conic sections. A memoir of suspension bridges. Therefore, the point F, defined above, is the focus of the parabola. Look up parabola in Wiktionary, the free dictionary.

A graph of a quadratic function is called a parabola. A parabola, according to Pascal, is a circular projection.

The logic of the last paragraph can be applied to modify the above proof of the reflective property. An alternative way is to determine the midpoints of two parallel chords, see section on parallel chords. They can be interpreted as Cartesian coordinates of the points D and E, in a system in the pink plane with P as its origin. An alternative way uses the inscribed angle theorem for parabolas. The lengths of BM and CM are:. Electromagnetism and Optics, lectures. This is the reflective property. The name "parabola" is due to Apollonius , who discovered many properties of conic sections. The diagram represents a cone with its axis AV. Extract of page 3. Let the line of symmetry intersect the parabola at point Q, and denote the focus as point F and its distance from point Q as f.