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Hyperbolas definitions

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  • Hyperbola
    A conic section with two separate curved branches opening away from each other, defined by a specific standard equation with a minus sign.
  • Conic Section
    A curve formed by the intersection of a plane and a double-napped cone, including shapes like circles, ellipses, parabolas, and hyperbolas.
  • Branch
    One of the two distinct curved parts of a hyperbola that extend infinitely and open in opposite directions.
  • Asymptote
    A straight line that a hyperbola's branch approaches but never touches, guiding the curve's direction.
  • Vertex
    A point where a branch of a hyperbola crosses the transverse axis, marking the closest approach to the center.
  • Transverse Axis
    The axis passing through the center and both vertices of a hyperbola, determining its orientation.
  • Center
    The midpoint between the vertices and foci of a hyperbola, serving as the reference point for its equation.
  • Focus
    A fixed point used to define a hyperbola, where the constant difference of distances from any point on the curve is measured.
  • Foci
    The two fixed points inside a hyperbola, used to maintain a constant difference in distances from any point on the curve.
  • Standard Form
    An equation format for hyperbolas, featuring squared terms and a minus sign, indicating orientation and center.
  • Horizontal Hyperbola
    A hyperbola with branches opening left and right, identified by the x-term appearing first in its standard equation.
  • Vertical Hyperbola
    A hyperbola with branches opening up and down, identified by the y-term appearing first in its standard equation.
  • Fundamental Rectangle
    A rectangle constructed using a and b values from the equation, whose diagonals determine the asymptotes.
  • Diagonal
    A line segment connecting opposite corners of the fundamental rectangle, used to draw asymptotes.
  • Orientation
    The direction in which a hyperbola opens, determined by which variable appears first in the standard form.
  • Equation
    A mathematical statement representing the relationship between x and y for a hyperbola, typically involving squared terms and a minus sign.
  • a-value
    The distance from the center to each vertex along the transverse axis, found under the leading squared term in the denominator.
  • b-value
    The distance from the center to the rectangle's edge perpendicular to the transverse axis, found under the second squared term.
  • Minus Sign
    A symbol in the standard form equation of a hyperbola, distinguishing it from an ellipse and indicating the curve's nature.
  • Origin
    The point (0,0) on the coordinate plane, often serving as the center for standard hyperbola equations.
  • Coordinate
    A pair of numerical values representing a point's position on the plane, used to locate the center or vertices.
  • Graph
    A visual representation of a hyperbola on the coordinate plane, showing branches, asymptotes, and key features.
  • Squared Term
    An expression where a variable is raised to the second power, as seen in the standard form of a hyperbola.