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. It was last seen in British general knowledge crossword.

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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An alternative way is to determine the midpoints of two parallel chords, see section on parallel chords. A parabola is determined by three points. Since SJ is the diameter, the center of the circle is at its midpoint, and it lies on the perpendicular bisector of SV, a distance of one half VJ from SV.

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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.

Poses de referencia

Therefore, the point F, defined above, is the focus of the parabola. The logic of the last paragraph can be applied to modify the above proof of the reflective property. The lengths of BM and CM are:. This is the reflective property. The above proofs of the reflective and tangent bisection properties use a line of calculus. Reversing the sign of p reverses the signs of h and s without changing their absolute values. If there is no generatrix parallel to the intersecting plane, the intersection curve will be an ellipse or a circle or a point. Since x is squared in the equation, the fact that D and E are on opposite sides of the y axis is unimportant. The reflective property follows as shown previously. In the following, the angle of two lines will be measured by the difference of the slopes of the line with respect to the directrix of the parabola. Here a geometric proof is presented. Therefore, light that enters the parabola and arrives at E travelling parallel to the axis of symmetry of the parabola is reflected by the parabola toward its focus. Compassion and godliness with no end of benevolence One doubting sign coat needs replacing In the field of transport, how would the French 'berline' and the German 'Limousine' generally be translated into British English? This is the principle behind the liquid-mirror telescope. Another chord BC is the perpendicular bisector of DE and is consequently a diameter of the circle.

A parabola is a graph of a quadratic function.

Therefore, this is the condition for the circle and parabola to coincide at and extremely close to the origin. Crossword Clues by Letters:. Bridge engineering: a global perspective. The above proofs of the reflective and tangent bisection properties use a line of calculus. 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. Thus, any parabola can be mapped to the unit parabola by a similarity. Reflecting Telescope Optics: Basic design theory and its historical development 2 ed. The area enclosed by a parabola and a line segment, the so-called "parabola segment", was computed by Archimedes by the method of exhaustion in the 3rd century BC, in his The Quadrature of the Parabola. Sponsored Links. The same effects occur with sound and other waves. Retrieved This is not in contradiction to the impossibility of an angle trisection with compass-and-straightedge constructions alone, as the use of parabolas is not allowed in the classic rules for compass-and-straightedge constructions. Therefore, light that enters the parabola and arrives at E travelling parallel to the axis of symmetry of the parabola is reflected by the parabola toward its focus. Since B is on the x axis, which is the tangent to the parabola at its vertex, it follows that the point of intersection between any tangent to a parabola and the perpendicular from the focus to that tangent lies on the line that is tangential to the parabola at its vertex. As in all cases in the physical world, the trajectory is always an approximation of a parabola.