11.1 Conics

11.1 Conics - The collection of all points P in the plane,...

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11.1: Conics The cone resembles an hour glass with the vertex as the center narrow point, the upper and lower parts are called nappes , and the sides (generators) are lines through the vertex that maintain and equal angle with the axis. Conic sections are curves that result from the intersection of the cone with a plane. Circle: plane is perpendicular to the axis. Ellipse: plane is tilted slightly, intersecting all generators but only one nappe. Parabola: plane is tilted so that plane is parallel to one generator and intersects only one nappe. Hyperbola: plane intersects both nappes. http://ccins.camosun.bc.ca/~jbritton/jbconics.htm Parabola: The collection of all points P in the plane that are the same distance from a fixed point F as they are from a fixed line D. Point F is the Focus and line D is the Directrix : d(F, P) = d(P, D). The line through the focus F and to the directrix D is the axis of symmetry. One variable is squared. Ellipse:
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Unformatted text preview: The collection of all points P in the plane, the sum of whose distances from two fixed points, called the foci ( F 1 and F 2 ), is a constant. The line containing the foci is the major axis ; the line through the center and to the major axis is the minor axis . Both the major and minor axis are each an axis of symmetry. Both variables are squared and added. Hyperbola: The collection of all points in the plane the difference of whose distances from two fixed points, called the foci , is constant. The line containing the foci is the transverse axis . The midpoint of the line segment joining the foci is the center of the hyperbola. The line through the center and to the transverse axis is the conjugate axis . The hyperbola consists of two separate branches . The points of intersection of the hyperbola and the transverse axis are the vertices, V 1 and V 2 . Both variables are squared and subtracted....
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