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Introduction to Conic Sections definitions Flashcards

Introduction to Conic Sections definitions
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  • Conic Section
    A two-dimensional shape formed by intersecting a cone with a plane at various angles.
  • Cone
    A three-dimensional geometric figure with a circular base tapering smoothly to a 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 conic section resulting from a horizontal slice through a cone, producing a perfectly round shape.
  • Ellipse
    A conic section formed by slicing a cone at a slight angle, creating an oval or stretched circle.
  • Parabola
    A conic section produced by slicing a cone at a heavily tilted angle, resulting in a U-shaped curve.
  • Hyperbola
    A conic section created by a vertical slice through a cone, resulting in two diverging curves.
  • Horizontal Slice
    A cut made parallel to the base of a cone, used to generate a circular conic section.
  • Slight Angle
    A small tilt of the plane relative to the cone's base, leading to the formation of an ellipse.
  • Heavily Tilted Angle
    A significant tilt of the plane, causing the intersection with the cone to produce a parabola.
  • Vertical Slice
    A cut made perpendicular to the base of a cone, resulting in a hyperbola with two separate curves.
  • Oval Shape
    A stretched, elongated form resembling an ellipse, distinct from a perfect circle.
  • Diverging Curves
    Two branches that move away from each other, characteristic of a hyperbola.
  • Equation
    A mathematical expression representing the relationship between variables for each conic section.
  • Graph
    A visual representation of a conic section, illustrating its unique shape and properties.