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Hyperbolas at the Origin definitions

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  • Hyperbola
    A conic section with two separate curves opening away from each other, defined by an equation with a minus sign between squared terms.
  • Conic Section
    A curve formed by the intersection of a plane and a double-napped cone, including circles, ellipses, parabolas, and hyperbolas.
  • Standard Form
    An equation format for hyperbolas: (x²/a²) - (y²/b²) = 1 or (y²/a²) - (x²/b²) = 1, with squared terms and denominators.
  • Center
    The midpoint of a hyperbola, often at the origin, from which distances to vertices, foci, and other features are measured.
  • Vertex
    A point on a hyperbola closest to the center, located a units away along the major axis.
  • Focus
    A point such that the absolute difference of distances from any point on the hyperbola to the two foci is constant.
  • Major Axis
    The axis along which the vertices and foci of a hyperbola are aligned, determining its orientation.
  • Minor Axis
    The axis perpendicular to the major axis, associated with the b value, used in constructing the graph and asymptotes.
  • Asymptote
    A straight line that the branches of a hyperbola approach but never touch, determined by a and b values.
  • Branch
    One of the two separate curves of a hyperbola, each opening away from the center and approaching asymptotes.
  • Orientation
    The direction in which a hyperbola opens, either horizontally (along x-axis) or vertically (along y-axis), based on the equation.
  • a Value
    The distance from the center to a vertex along the major axis, always associated with the first denominator in standard form.
  • b Value
    A measurement used to determine the height of the box for graphing and the slopes of asymptotes, found in the second denominator.
  • c Value
    The distance from the center to a focus, calculated using c² = a² + b² for hyperbolas.
  • Box Method
    A graphing technique where a rectangle is drawn using a and b values to help locate asymptotes and sketch the hyperbola.