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Hyperbolas NOT at the Origin definitions

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  • Hyperbola
    A conic section with two separate branches, defined by a specific quadratic equation involving subtraction of squared terms.
  • Conic Sections
    The four main curves—circle, ellipse, parabola, and hyperbola—formed by intersecting a plane with a cone.
  • Standard Equation
    A mathematical form representing a hyperbola, modified by shifting parameters to indicate its center.
  • Center
    The point (h, k) indicating the location around which a hyperbola is symmetrically arranged.
  • Horizontal Shift
    A movement of the hyperbola along the x-axis, determined by the value subtracted from x in the equation.
  • Vertical Shift
    A movement of the hyperbola along the y-axis, determined by the value subtracted from y in the equation.
  • Vertices
    The two points on a hyperbola closest to or farthest from the center, found by adjusting one coordinate by 'a'.
  • Asymptotes
    Diagonal lines that the branches of a hyperbola approach but never touch, aiding in sketching the curve.
  • Foci
    Two fixed points inside each branch of a hyperbola, located using the relationship c² = a² + b².
  • Branches
    The two separate, mirror-image curves that make up a hyperbola, each approaching the asymptotes.
  • a Value
    The positive square root of the denominator under the leading squared term, used to find vertices.
  • b Value
    The positive square root of the denominator under the second squared term, used to find 'b' points.
  • c Value
    The distance from the center to each focus, calculated using c² = a² + b².
  • Box Method
    A graphical technique using a rectangle formed by vertices and 'b' points to help draw asymptotes.
  • Vertical Hyperbola
    A hyperbola oriented so its branches open up and down, indicated when the y-term appears first in the equation.