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Ellipses: Standard Form definitions

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Termini in questo insieme (15)

  • Ellipse
    A conic section formed by slicing a cone at a slight angle, resulting in a closed, oval-shaped curve with two axes of different lengths.
  • Conic Section
    A curve obtained by intersecting a cone with a plane, producing shapes like circles, ellipses, parabolas, and hyperbolas.
  • Semi-Major Axis
    The longest radius of an ellipse, extending from the center to the furthest point on the curve along the major axis.
  • Semi-Minor Axis
    The shortest radius of an ellipse, extending from the center to the closest point on the curve along the minor axis.
  • Major Axis
    The longest diameter of an ellipse, passing through its center and both vertices, aligned with the semi-major axis.
  • Minor Axis
    The shortest diameter of an ellipse, passing through its center and perpendicular to the major axis.
  • Vertex
    A point on an ellipse located at the maximum distance from the center along the major axis.
  • Foci
    Two fixed points inside an ellipse where the sum of the distances to any point on the ellipse remains constant.
  • Center
    The midpoint of both the major and minor axes of an ellipse, serving as the reference for its position.
  • Standard Form
    An equation format for ellipses, showing squared terms of x and y divided by squared axis lengths, set equal to one.
  • Orientation
    The direction in which the major axis of an ellipse is aligned, either horizontally or vertically.
  • Denominator
    The value under each squared variable in the ellipse equation, representing the square of the corresponding axis length.
  • Shift
    A translation of the ellipse's center from the origin to a new point, indicated by h and k in the equation.
  • C Value
    The distance from the center of an ellipse to each focus, calculated using the relationship c² = a² - b².
  • Function Transformation
    A change in the position or shape of a graph, such as shifting the center of an ellipse using h and k.