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Introduction to Conic Sections definitions

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  • Conic Section
    A shape formed by intersecting a three-dimensional cone with a two-dimensional plane at various angles.
  • Cone
    A three-dimensional geometric figure with a circular base tapering smoothly to a single point called the apex.
  • Plane
    A flat, two-dimensional surface that extends infinitely in all directions and can intersect a cone to form conic sections.
  • Circle
    A round shape resulting from a horizontal slice through a cone, where all points are equidistant from the center.
  • Ellipse
    An oval-shaped curve formed by slicing a cone at a slight angle, resembling a stretched circle.
  • Parabola
    A curved, open shape produced by slicing a cone with a heavily tilted plane, often seen in graphs of quadratic functions.
  • Hyperbola
    A pair of diverging curves created by a vertical slice through a cone, resulting in two separate branches.
  • Horizontal Slice
    A cut made parallel to the base of a cone, producing a circular cross-section.
  • Vertical Slice
    A cut made perpendicular to the base of a cone, resulting in a hyperbola.
  • Slicing Angle
    The orientation of the plane relative to the cone, determining which conic section is formed.
  • Equation
    A mathematical expression representing the relationship between variables for each conic section.
  • Apex
    The pointed tip of a cone where all straight lines from the base converge.
  • Diverging Curves
    Two branches that move away from each other, characteristic of a hyperbola.
  • Memory Tool
    A conceptual aid, such as the slicing analogy, used to help visualize and recall conic section types.