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Topic: Directrix

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	PlanetMath: conic section
		The definition in terms of a focus and a directrix leaves out the case of a circle; still, the circle can be thought of as a limiting case: eccentricity zero, directrix at infinity, and two coincident foci.
		The chord through the given focus, parallel to the directrix, is called the latus rectum; its length is traditionally denoted by
		A projective conic has no focus, directrix, or eccentricity, for in a projective plane there is no notion of distance (nor angle).
	planetmath.org /encyclopedia/Directrix.html (818 words)

	Parabolas in Suspension Bridges! Oh, my!
		A parabola is a set of all points that are the same distance from a fixed line (directrix) and a fixed point (focus) not on the directrix.
		The vertex is also the midpoint of the segment of the axis between the focus and the directrix.
		Indicates how far the directrix and the focus are from the vertex, because they are both equidistant from the vertex.
	www.carondelet.pvt.k12.ca.us /Family/Math/03210/page2.htm (398 words)

	PlanetMath: parabola
		To obtain a simple equation for the parabola, assume that the directrix is parallel to the
		-axis, and the directrix and focus are the same distance from the origin.
		, the distance between the focus and the directrix.
	planetmath.org /encyclopedia/Directrix3.html (265 words)

	[No title]
		The vertex of a parabola lies halfway between the directrix and the focus.
		The directrix for the original parabola would have had the form x = p, so using the x-coordinate from the new vertex, I will add 3 to it and set it equal to x.
		The directrix for the original parabola has the form y = - p, so using the y-coordinate from the vertex, I will subtract p from it.
	faculty.eicc.edu /bwood/ma155supplemental/supplemental29.htm (1657 words)

	Parabolas
		Then the directrix, being perpendicular to the axis, is a horizontal line and it must be p units away from V. The directrix then is the line y=-p.
		Consider a point P with coordinates (x,y) on the parabola and let Q be the point on the directrix such that the line through PQ is perpendicular to the directrix.
		From this, we should be able to recognize the coordinates of the vertex and the focus as well as the equation of the directrix.
	colalg.math.csusb.edu /~devel/precalcdemo/conics/src/parabola.html (807 words)

	parabolic reflectors
		The focus and directrix of each parabola was marked on the graph along with the corresponding equation of the parabola.
		The focus of the graph is (0,1) and the directrix is y = -1.
		The focus of the graph is (0,2) and the directrix is y = -2.
	nths.newtrier.k12.il.us /academics/math/Connections/reflection/pararefl.htm (321 words)

	Polar Equations for Conics
		The locus of a point in the plane that moves so that its distance from a fixed point (focus) is in constant ratio to its distance from a fixed line (directrix) is a conic.
		is the distance between the pole and the directrix.
		Therefore, the graph is an ellipse with directrix 3/8 units above the pole (a focal point).
	www.mecca.org /~halfacre/MATH/polarconics.htm (335 words)

	Center for Technology and Teacher Education: Mathematics Activities (Site not responding. Last check: 2007-10-12)
		directrix - a fixed line that is the same distance as the focus from each point on the parabola.
		We are interested in the pattern of the creases that are formed when point F is folded along the directrix.
		Manipulate the locations of the directrix and the focus to classify the movement of the graph.
	www.teacherlink.org /content/math/activities/skpv4-parabola/guide.html (1352 words)

	PH@School: Mathematics: Algebra 2: Chapter 10 Extra Help
		The directrix is y = 5 – 1, or y = 4.
		Since the directrix is a vertical line to the left of the focus, the parabola opens to the right.
		The directrix is thus 4 units in the positive direction from the vertex, or y = 8.
	www.phschool.com /atschool/ph_algebra/Algebra2/Student_Area/ALG2_SC10_EH_5.html (266 words)

	Sample Contracts and Business Forms - CA-Los Angeles-3030 Andrita Street Sublease - Playboy Entertainment Group Inc. ...
		Directrix' Share of the Operating Expenses and any other charges hereunder shall be referred to as the "Sublease Additional Rent." The obligation of Directrix to pay the Sublease Additional Rent shall survive the expiration of the Term.
		Directrix shall be entitled to use without charge 30 unreserved parking spaces on those portions of the Common Areas to be agreed to by Playboy and Directrix.
		Directrix shall not permit or allow any vehicles that belong to or are controlled by Directrix or Directrix' employees, suppliers, shippers, customers, contractors or invitees to be loaded, unloaded, or parked in areas other than those designated by Playboy for such activities.
	contracts.onecle.com /playboy/andrita.sublease.2001.09.20.shtml (2729 words)

	Parabola
		A parabola can also be defined as locus of points which are equidistant from a given point (the focus) and a given line (the directrix).
		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.brainyencyclopedia.com /encyclopedia/p/pa/parabola.html (764 words)

	directrix (Site not responding. Last check: 2007-10-12)
		The fixed point is the focus of the conic, the fixed line the directrix, and the constant ratio the eccentricity.
		In the graphic below, the focus is fixed at the origin and the directrix is movable using the arrows or the play button.
		Notice the distance from the focus to conic along the y-axis and its corresponding distance from that point to the directrix are colored to represent the changing eccentricity.
	www.wmchs.org /USERS/gmagliaro/orbitdemo.htm (111 words)

	Parabola
		It can be observed (and of course proven from the focal definition or, as easily, from the canonical or polar equation) that parabola has an axis of symmetry which passes through the focus perpendicular to the directrix.
		The point midway between the focus and the directrix is an extremity of the parabola, known as its apex.
		This exactly means that the directrix is the polar of the focus, while the focus is the pole of the directrix with respect to the parabola.
	www.cut-the-knot.org /ctk/Parabola.shtml (2812 words)

	[No title]
		This plane(line) is called the directrix, and it is perpencidular to a line drawn through the apex of the parabola to the focus.
		Note that the distance from the point on the parabola to the directrix is the closest distance, or the perpendicular distance to the plane(line).
		Thus the apex is equidistant from the focus and the directrix and is on the parabola!
	www.armory.com /~rstevew/Public/Tutor/Math/ParabolicDish.txt (1198 words)

	Assignments (Site not responding. Last check: 2007-10-12)
		A parabola with focus at F(0,a) and directrix y = -a is the set of all points P(x,y) such that the distance from P to F is equal to the distance from P to the directrix.
		What is the distance from the directrix to P? If the focus had been at (0, a) and the directrix at y = -a, how would the equation have been changed?
		(b) focus at (0,6), directrix at y = -6.
	etsuodt.tamu-commerce.edu /coas/math/FACULTY/anderson/hmk-041122.html (923 words)

	Plane Graphic Calculator Gallery 1: Conic Sections
		The curvature of a parabola depends on the distance between its focus and its directrix.
		For all ellipses, the distance between k and the focus is a constant fraction of the distance between k and the directrix.
		For all hyperbolas, the distance between k and the focus is a constant multiple of the distance between k and the directrix.
	www.accesscom.com /~lillge/pgc/pgc-gallery1.shtml (997 words)

	Parabolas
		A parabola is a set of points in the plane that are equidistant from a given line, called the directrix and a given point not on the directrix, called the focus.
		The focus thus lies a distance 2 p from the directrix.
		Given the equation of a parabola, be able to put it into standard form by completing the square and be able to find the coordinates of its vertex, focus and the endpoints of the focal chord.
	jwbales.home.mindspring.com /precal/part9/part9.1.html (760 words)

	Math 108 Chapter 9
		There you know what the distance from the directrix is, it is 2p, so you can get two more points by going to the right and left of the focus a distance of 2p.
		The focus is p to the right of the vertex and the directrix is p to the left of the directrix.
		Since the focus is to the right of the directrix we know the equation is of the type where the squared part has a y in it.
	faculty.ed.umuc.edu /~swalsh/UM/M108Ch9.html (4326 words)

	Construct a Parabola
		The axis of the parabola is the line through F and perpendicular to the directrix.
		Point V on the axis and halfway between the focus F and the directrix is called the vertex.
		Point D on the directrix and has the same y-coordinate as point M. The distances d(F,M) and d(D,M) are both equal to 2.
	www.analyzemath.com /parabola/ParabolaDefinition.html (665 words)

	Quandaries & Queries at Math Central
		I working on a problem that asks me to give the equation of an ellipse when only the location of the directrix and the length of the latus rectum are given.
		I note that the latus rectum segment is unique in one respect in that it is parallel to the directrix, where any other line segment on the ellipse to the focus would not be.
		Consider a ray of light that passes through a chord of a parabola (the chord is above the focus and parallel to the directrix), hits the parabola at a point (x,y) and is reflected through the focus.
	mathcentral.uregina.ca /QandQ/topics/directrix (248 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.
		The x-axis lies midway between the focus and the directrix.
	www.cut-the-knot.com /Curriculum/Geometry/ParabolaEnvelope.shtml (454 words)

	Parabola equation with focus and directrix - Information Technology Services (Site not responding. Last check: 2007-10-12)
		I made two distance equations one for any point on the parabola to the focus, and one distance from the directrix to any point on the parabola.
		A parabola is defined as the set of points such that the distance from each point (x,y) to the focus is the same as the distance from (x,y) to the directrix.
		Since, in this problem, the directrix is a horizontal line, the axis of the parabola is vertical.
	www.physicsforums.com /archive/t-69327_Parabola_equation_with_focus_and_directrix.html (386 words)

	conicas (Site not responding. Last check: 2007-10-12)
		The conics can be defined in terms of one of their foci, of a straight line called directrix and a number called eccentricity.
		The locus of the points such that the ratio of the distance to the focus and the distance to the directrix is equal to the eccentricity, is a conic curve.
		There is another special form for conic sections based on the focus, the directrix and a point of the curve.
	www.pntic.mec.es /Descartes/Ingles/conicas_avanzadas.htm (170 words)

	The CTK Exchange Forums
		A parabola is defined by a point (the focus) and a line (the directrix).
		The dot is the focus, and the line is the directrix.
		They had to draw it somehow, and the directrix was probably a very convenient way of accomplishing this.
	www.cut-the-knot.com /htdocs/dcforum/DCForumID3/288.shtml (211 words)

	The Ellipse (Site not responding. Last check: 2007-10-12)
		Place the center of the ellipse at the origin so that one focus lies at (- ae,0) and one directrix is the line x = - ale.
		If the point (x,y) is on the ellipse, then the ratio of its distance from F to its distance from the directrix is e.
		Whenever the directrix is a line denoted by the equation y = k, the major axis is in the y direction and the equation of the ellipse is as follows:
	www.tpub.com /math2/15.htm (654 words)

	Directrix, Inc. - Fact Sheet - Hoover's (Site not responding. Last check: 2007-10-12)
		Directrix was spun off from Spice Entertainment in 1999, following Spice's merger with Playboy.
		Playboy abruptly canceled its 15-year contract with Directrix in which Directrix would provide commercial space and technical services to Playboy.
		Directrix sank into Chapter 11 and sued the adult entertainment icon for breach of contract.
	www.hoovers.com /directrix/--ID__58476--/free-co-factsheet.xhtml (205 words)

	Parabolas in GSP/JSP
		Now move the focus point further or closer from the directrix (click the red X again to clear the traced lines) and drag the point on the directrix again or press the show animate button-button and try the animation.
		Notice that the distance from the focus to the point of the locus is equal to the distance from the locus point to the point on the directrix.
		A parabola is a collection of points (a locus) such that the moving locus point is always equidistant from the focus and the directrix.
	www.mste.uiuc.edu /dildine/sketches/parabola.htm (636 words)

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