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    Take a right circular cone of semi-vertical angle \alpha with the axis of the cone along the z-axis.

    Now, at a point P on the surface of the cone where the radius is r, form an ellipse via the intersection of the surface of the cone and the plane that is normal to the surface of the cone and parallel to the x-axis at P.

    What is the radius of curvature of this cone at its vertices, in terms of r?

    Anyone got a nice solution?
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    (Original post by atsruser)
    Take a right circular cone of semi-vertical angle \alpha with the axis of the cone along the z-axis.

    Now, at a point P on the surface of the cone where the radius is r, form an ellipse via the intersection of the surface of the cone and the plane that is normal to the surface of the cone and parallel to the x-axis at P.

    What is the radius of curvature of this cone at its vertices, in terms of r?

    Anyone got a nice solution?
    I am having difficulty visualising...
    (any chance of a drawing?)
 
 
 
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