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# Radius of curvature of an ellipse watch

1. Take a right circular cone of semi-vertical angle 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 , 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 ?

Anyone got a nice solution?
2. (Original post by atsruser)
Take a right circular cone of semi-vertical angle 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 , 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 ?

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

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