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Math Help - Conic section question, intersection with plane!

  1. #1
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    Conic section question, intersection with plane!

    How do you find the points of intersection between a cone and a plane.
    The points on the plane form a hyperbola.
    The image is of cone with different opening angles.
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  2. #2
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    Do you have equations for the cone and plane? Getting them on a coordinate axis system would be a good start. If nothing else, it will capacitate an algebraic solution.
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  3. #3
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    equation for the cone is ax^2+bz^2=cy^2
    equation for the plane is z=h

    the cone is defined by the variables a,b and c.
    the plane intersects the cone z=h

    I'm looking for an equation which defines the hyperbolas which are the points where the cone intersects the plane.

    Thanks!
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