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.

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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The focus does not lie on the directrix.

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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.

A plane curve in mathematics that is approximately u-shaped

A parabola is a graph of a quadratic function. Pascal stated that a parabola is a projection of a circle. Galileo explained that projectiles falling under the effect of uniform gravity follow a path called a parabolic path. Many physical motions of bodies follow a curvilinear path which is in the shape of a parabola.

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ISBN Another definition of a parabola uses affine transformations :. In nature, approximations of parabolas and paraboloids are found in many diverse situations. You can search by using the letters you already have! In other words, the tangent to the parabola at any point bisects the angle between the lines joining the point to the focus and perpendicularly to the directrix. Let's take an example pattern: "d? Remark: The 3-pointstangent-property of a parabola is an affine version of the 4-point-degeneration of Pascal's theorem. In other projects. Knowles December Main article: Orthoptic geometry. The parabolic orbit is the degenerate intermediate case between those two types of ideal orbit.

A graph of a quadratic function is called a parabola.

Authority control databases : National Israel Czech Republic. O is center. Sponsored Links. The proof is a consequence of the de Casteljau algorithm for a Bezier curve of degree 2. National Mathematics Magazine. The lengths of BM and CM are:. Often, as here, they are drawn parallel with the parabola's axis of symmetry, but this is arbitrary. Let the perpendicular to the line of symmetry, through the focus, intersect the parabola at a point T. By Book 1, Proposition 16, Corollary 6 of Newton's Principia , the speed of a body moving along a parabola with a force directed towards the focus is inversely proportional to the square root of the radius. This shows that these two descriptions are equivalent. According to the definition of a parabola as a conic section, the boundary of this pink cross-section EPD is a parabola. The name "parabola" is due to Apollonius , who discovered many properties of conic sections. In this case, the centrifugal force causes the liquid to climb the walls of the container, forming a parabolic surface. Application: This property can be used to determine the direction of the axis of a parabola, if two points and their tangents are given.