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10.7.1: Key Terms

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    Key Terms

    angle of rotation
    an acute angle formed by a set of axes rotated from the Cartesian plane where, if cot( 2θ )>0, cot( 2θ )>0, then θ θ is between (,45°); (,45°); if cot(2θ)<0, cot(2θ)<0, then θ θ is between (45°,90°); (45°,90°); and if cot( 2θ )=0, cot( 2θ )=0, then θ=45° θ=45°
    center of a hyperbola
    the midpoint of both the transverse and conjugate axes of a hyperbola
    center of an ellipse
    the midpoint of both the major and minor axes
    conic section
    any shape resulting from the intersection of a right circular cone with a plane
    conjugate axis
    the axis of a hyperbola that is perpendicular to the transverse axis and has the co-vertices as its endpoints
    degenerate conic sections
    any of the possible shapes formed when a plane intersects a double cone through the apex. Types of degenerate conic sections include a point, a line, and intersecting lines.
    a line perpendicular to the axis of symmetry of a parabola; a line such that the ratio of the distance between the points on the conic and the focus to the distance to the directrix is constant
    the ratio of the distances from a point P P on the graph to the focus F F and to the directrix D D represented by e= PF PD , e= PF PD , where e e is a positive real number
    the set of all points ( x,y ) ( x,y ) in a plane such that the sum of their distances from two fixed points is a constant
    plural of focus
    focus (of a parabola)
    a fixed point in the interior of a parabola that lies on the axis of symmetry
    focus (of an ellipse)
    one of the two fixed points on the major axis of an ellipse such that the sum of the distances from these points to any point ( x,y ) ( x,y ) on the ellipse is a constant
    the set of all points ( x,y ) ( x,y ) in a plane such that the difference of the distances between ( x,y ) ( x,y ) and the foci is a positive constant
    latus rectum
    the line segment that passes through the focus of a parabola parallel to the directrix, with endpoints on the parabola
    major axis
    the longer of the two axes of an ellipse
    minor axis
    the shorter of the two axes of an ellipse
    nondegenerate conic section
    a shape formed by the intersection of a plane with a double right cone such that the plane does not pass through the apex; nondegenerate conics include circles, ellipses, hyperbolas, and parabolas
    the set of all points ( x,y ) ( x,y ) in a plane that are the same distance from a fixed line, called the directrix, and a fixed point (the focus) not on the directrix
    polar equation
    an equation of a curve in polar coordinates r r and θ θ
    transverse axis
    the axis of a hyperbola that includes the foci and has the vertices as its endpoints

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