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Hyperbolas at the Origin definitions Flashcards

Hyperbolas at the Origin definitions
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  • Hyperbola
    A conic section with two separate curves opening away from each other, defined by a standard equation with a minus sign between squared terms.
  • Ellipse
    A conic section similar in equation to a hyperbola but with a plus sign, forming a closed, oval-shaped curve.
  • 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.
  • Major Axis
    The axis along which the vertices and foci of a hyperbola or ellipse are aligned, determined by the a value.
  • Minor Axis
    The axis perpendicular to the major axis, associated with the b value in hyperbolas and ellipses.
  • Vertex
    A point on a hyperbola closest to the center, located a units from the center along the major axis.
  • Focus
    A point such that the difference of distances from any point on the hyperbola to each focus is constant.
  • Asymptote
    A straight line that the branches of a hyperbola approach but never touch, determined by the slopes a/b or b/a.
  • Orientation
    The direction in which a hyperbola opens, either horizontally (along x-axis) or vertically (along y-axis), based on the equation.
  • Center
    The midpoint of a hyperbola, typically at the origin, from which distances to vertices and foci are measured.
  • Branch
    One of the two separate curves that make up a hyperbola, each extending infinitely and approaching asymptotes.
  • Box Method
    A graphing technique using a rectangle defined by a and b values to help draw asymptotes and the hyperbola.
  • Slope
    A measure of steepness for asymptotes, calculated as rise over run using a and b values from the hyperbola's equation.
  • Standard Equation
    A formula for hyperbolas at the origin, distinguishing horizontal and vertical cases by the placement of x² and y².