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Ellipse from cone

  1. Jul 13, 2010 #1
    Hi,

    If the cone is cut with a plane such that an ellipse has been formed. Let's say the major axis is 'a' and the minor axis is 'b'.

    Is there a way to find a and b from the geometry instead of getting them from the quadratic equation.
     
  2. jcsd
  3. Jul 14, 2010 #2
    The inclination of the plane would give the ratio a:b & its distance from the vertex of the cone would give a. I would prefer to do this trigonometrically.
     
  4. Jul 14, 2010 #3
    Thank you ... But can you give me an example.
     
  5. Jul 14, 2010 #4
    The distance of the plane from the vertex of the cone as measured along the axis of the cone and the slope of the cone determines the semi-minor axis of the ellipse, while the inclination of the plane together with that distance determines the semi-major axis.
     
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