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Topic: Parabola

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Tangent plane

Locus (mathematics)

Paraboloid

Line (mathematics)

Plane (mathematics)

Conic section

Parabolic mirror

Parabolic reflector

Spherical reflector

Exterior covariant derivative

Hyperbola

Ellipse

Quadratic function

Derivation of the cartesian formula for an ellipse

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	Parabola - LoveToKnow 1911 (Site not responding. Last check: 2007-10-20)
		The parabola is the curve described by a projectile which moves in a non-resisting medium under the influence of gravity (see Mechanics).
		The orthocentre of a triangle circumscribing a parabola is on the directrix; a deduction from this theorem is that the centre of the circumcircle of a self-conjugate triangle is on the directrix ("Steiner's Theorem").
		The cartesian equation to a parabola which touches the coordinate axes is 1 / ax+'1 / by= i, and the polar equation when the focus is the pole and the axis the initial line is r cos 2 6/2 = a.
	www.1911encyclopedia.org /Parabola (1653 words)

	Parabola as envelope of lines
		Parabola is a conic defined by its focal property: there is a point - focus - and a line - directrix - and parabola is the locus of points equidistant from the focus and the directrix.
		It is known that the tangent to parabola at a point bisects the angle between the segments joining the point to the focus and the directrix.
		This is the parabola with focus F and the apex on the x-axis.
	www.cut-the-knot.org /Curriculum/Geometry/ParabolaEnvelope.shtml (500 words)

	Parabola
		The pedal of the parabola with its vertex as pedal point is a cissoid.
		The evolute of the parabola is Neile's parabola.
		The caustic of the parabola with the rays perpendicular to the axis of the parabola is Tschirnhaus's Cubic.
	www-groups.dcs.st-and.ac.uk /~history/Curves/Parabola.html (327 words)

	parabola
		One of the most studied curves in the history of mathematics, a parabola is the outline of the figure obtained if a right circular cone is cut by a plane that is exactly parallel to the cone's side.
		Just as the circle is a limiting case of the ellipse when the two foci coincide, the parabola is a limiting case of the ellipse when one of the foci is moved to infinity.
		A parabola is the locus of all points in a plane that are equidistant from a given line, known as the directric, and a given point not on the line, known as the focus.
	www.daviddarling.info /encyclopedia/P/parabola.html (584 words)

	Parabola
		A parabola is a conic section generated by the intersection of a cone, and a plane tangent to the cone or parallel to some plane tangent to the cone.
		A parabola can also be obtained as the limit of a sequence of ellipses where one focus is kept fixed as the other is allowed to move arbitrarily far away in one direction.
		A parabola has a single axis of reflective symmetry, which passes through its focus and is perpendicular to its directrix.
	www.guajara.com /wiki/en/wikipedia/p/pa/parabola.html (739 words)

	Parabola
		are parallel to the axes of the parabola.
		As we saw earlier, x-axis is the pedal curve of the parabola with respect to its focus.
		Two tangents of a parabola are divided into segments of like proportion by a third and this third is divided in the same proportion by its point of tangency [Dörrie, p.
	www.cut-the-knot.org /ctk/Parabola.shtml (2812 words)

	Parabola Summary
		The parabola (from the Greek: παραβολή) is a conic section generated by the intersection of a right circular conical surface and a plane parallel to a generating straight line of that surface.
		The parabola is an inverse transform of a cardioid.
		The most well-known instance of the parabola in the history of physics is the trajectory of a particle or body in motion under the influence of a uniform gravitational field without air resistance (for instance, a baseball flying through the air, neglecting air friction).
	www.bookrags.com /Parabola (2257 words)

	Xah: Special Plane Curves: Parabola
		Vertex of the parabola is the intersection of the parabola and its axis.
		The pedal of a parabola with respect to its focus is a line; pedal with respect to its vertex is the cissoid of Diocles.
		The inversion of a parabola with respect to its focus is a cardioid; inversion with respect to its vertex is the cissoid of Diocles.
	xahlee.org /SpecialPlaneCurves_dir/Parabola_dir/parabola.html (507 words)

	PARABOLA - Online Information article about PARABOLA (Site not responding. Last check: 2007-10-20)
		For example, in trilinear co-ordinates, the equation to the general conic circumscribing the triangle of reference is l0y+mya+naf=o; for this to be a parabola the line as + b/3 + cy=o must be a tangent.
		biquadratic parabola; semi parabolas have the general equation axn-1=yn, thus ax2=y3 is the semicubical parabola and ax3=y4 the semibiquadratic parabola.
		Newton showed that all the five varieties of the diverging parabolas may be exhibited as plane sections of the solid of revolution of the semi-cubical parabola.
	encyclopedia.jrank.org /PAI_PAS/PARABOLA.html (1881 words)

	Parabola
		The point of intersection of the parabola and its line of symmetry is the vertex of the parabola and is the lowest or highest point of the graph.
		The vertex of the parabola is the point of the parabola that is closet to both the focus and directrix.
		Therefore, the parabola is one with a horizontal line of symmetry and opens to the left.
	www.personal.kent.edu /~rmuhamma/Algorithms/MyAlgorithms/parabola.htm (506 words)

	The Parabola
		In the parabola shown in figure 2-8, point V, which lies halfway between the focus and the directrix, is called the vertex of the parabola.
		In this figure and in many of the parabolas discussed in the first portion of this section, the vertex of the parabola falls at the origin; however, the vertex of the parabola, like the center of the circle, can fall at any point in the plane.
		The focal chord is one of the properties of a parabola used in the analysis of a parabola or in the sketching of a parabola.
	www.tpub.com /math2/13.htm (712 words)

	PlanetMath: conic section
		Any ellipse other than a circle, or any hyperbola, may be defined by either of two focus-directrix pairs; the eccentricity is the same for both.
		To work with conic sections in such an astronomical context, it is very useful to have a description in terms of polar coordinates centered at one focus.
		A parabola or hyperbola can also be described in an essentially similar way, although they do not have a semi-major axis.
	planetmath.org /encyclopedia/Parabola.html (818 words)

	Chapter 8
		A parabola is the locus of a point that moves so that its distances from a fixed line and a fixed point are equal.
		A parabola (see Figure 8.7b) can be defined as any section of a right circular cone resulting from a plane slicing through the cone parallel to, but not including, the axis of the cone.
		The equation of the tangent to this parabola at
	www.powerfromthesun.net /Chapter8/Chapter8new.htm (3499 words)

	The Geometry of the Parabola
		Parabolas are a central topic in high school algebra classes, but, perhaps because of the rigid separation between algebra and geometry classes in the US secondary curriculum, we do not usually treat them as geometric objects.
		A light ray originating at the focus will be reflected on the parabola and continue in a direction parallel to the axis of symmetry.
		Exercise: Prove the reflection property of the parabola, assuming that the angles of incidence and reflection are determined with respect to the tangent to the parabola at the point of incidence.
	www.picciotto.org /math-ed/parabolas/geometry/index.html (700 words)

	Parabola Data (FIFE)
		PARABOLA measurements were made during each of the 5 FIFE Intensive Field Campaigns from five locations within the FIFE study area.
		The PARABOLA, is an instrument specifically designed to measure variations in vegetation reflectance as a function of solar and sensor viewing geometry, wavelength, and plant canopy biophysical characteristics.
		Since the PARABOLA observations are not acquired at equal angles of azimuth and zenith, and since most users prefer the data at equal intervals, this data has been averaged into standard bins.
	www-eosdis.ornl.gov /FIFE/Datasets/Surface_Radiation/Parabola_Data.html (4721 words)

	Earth Math
		A parabola which opens up has a lowest point and a parabola which opens down has a highest point.
		The graph of this function is a parabola opening downward and the maximum value of the function is 11.
		Since the parabola is symmetric with respect to a vertical line through its vertex (the axis of symmetry) the x-coordinate of the vertex is always halfway between the two x-intercepts.
	earthmath.kennesaw.edu /main_site/review_topics/vertex_of_parabola.htm (735 words)

	The GNU 3DLDF Parabolae Page
		The Intersection of a Parabola and a Linear Path
		The intersection points of a parabola p and a line seqment l such that p and l are coplanar.
		The Intersection of a Parabola and a Plane
	www.gnu.org /software/3dldf/parabola.html (558 words)

	Parabola Learning Plan (Site not responding. Last check: 2007-10-20)
		If time permits, do analogous construction on geometer’s sketchpad, match to graph to confirm that this is indeed a parabola.
		Parabola construction from connecting dots on intersecting lines (enrichment)—either with paper and pencil or geometer’s sketchpad.
		Describe a parabola or parabaloid from the “real world”, and how its shape is important to its function.
	users2.ev1.net /~charliehb/RUSMP/ParabolaLearningPlan.htm (296 words)

	Parabola
		The parabola is probably the most important of the three conic curves (ellipse, parabola, and hyperbola) in terms of everyday use.
		Since the eccentricity of a parabola is 1, the vertex is equidistant from the directrix and focus (vD = vF).
		Points on the parabola are indicated where the arc intersects the line that parallels the directrix.
	personal.atl.bellsouth.net /e/d/edwin222/parabola1.htm (699 words)

	Parabola
		which represents an ellipse, a parabola, or a hyperbola depending on whether q is less than, equal to, or greater than 0.
		The triangles formed by two tangents to a parabola and the chord connecting the points of tangency were used by Archimedes in his study of the area of parabolic segments and bear his name.
		Parabola as Envelope II Assume a parabola with two points A and B and their tangents AS and BS are given.
	www.maa.org /editorial/knot/Parabola.html (2536 words)

	parabola
		The word 'parabola' refers to the parallelism of the conic section and the tangent of the conic mantle.
		In the parabola curve the parabola (with its vertex oriented downwards) is being repeated infinitely.
		In the case of a chord without lamps, instead of a parabola, a catenary is formed.
	www.2dcurves.com /conicsection/conicsectionp.html (759 words)

	Parabola Trust
		Parabola is a commissioning and curatorial body dedicated to the production of contemporary art and critical debate.
		Through its exhibitions, publications and events, Parabola attempts to invigorate dialogues between different groups and disciplines, from architecture and new technologies, to museological practice and the interpretation of histories.
		Parabola’s exhibition is multi-layered: it brings pieces of the original Tradescant cabinet from the Ashmolean Museum and the Museum of the History of Science, Oxford, back to Lambeth to be considered by a new audience.
	www.parabolatrust.org (334 words)

	Notes on Laying Out a Parabola
		For a parabola that is to be 96 inches across (that is, -48 inches to +48 inches relative to the focal point) and 48 inches deep, with a focal point 12 inches above the bottom of the parabola, the formula generates the numbers shown in the table on the right.
		where x is the width (from the focal point) of the parabola, y is the depth of the parabola, and f is the distance ahead of the bottom of the parabola of the focal point.
		In this case, the parabola will be 96 inches wide and 48 inches deep, with the focal (marked with a circle) point 12" in front of the bottom.
	www.gizmology.net /parabola.htm (326 words)

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