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Ellipses: Standard Form definitions

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  • Ellipse
    A conic section formed by slicing a cone at an angle, resulting in a closed, oval shape defined by 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.
  • Semi-Minor Axis
    The shortest radius of an ellipse, extending from the center to the closest point on the curve.
  • Horizontal Ellipse
    An ellipse oriented so its major axis runs left to right, with the larger denominator under the x-term in its equation.
  • Vertical Ellipse
    An ellipse oriented so its major axis runs up and down, with the larger denominator under the y-term in its equation.
  • Standard Form
    An equation format for ellipses showing squared terms of x and y divided by squared axes lengths, set equal to one.
  • Center
    The midpoint of an ellipse, located at (h, k) in the shifted standard form equation.
  • Vertex
    A point on the ellipse located at the ends of the major axis, representing the maximum distance from the center.
  • Focus
    One of two fixed points inside an ellipse where the sum of distances to any point on the curve remains constant.
  • Major Axis
    The longest line segment passing through the center and both vertices of an ellipse.
  • Minor Axis
    The shortest line segment passing through the center and both endpoints perpendicular to the major axis.
  • Denominator
    The squared value under each variable in the standard form equation, representing the square of the axis length.
  • Distance c
    The value found using c² = a² - b², representing the distance from the center to each focus along the major axis.
  • Function Transformation
    A shift or change in the graph of an equation, such as moving the center of an ellipse from the origin to (h, k).