Circular Hole Drilled in a Cone

This Demonstration lets you explore the shape of the difference between a cone and a circular cylinder.

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DETAILS

Consider a cylinder of radius , with axis at a distance from the axis and at a height above the - plane. Its parametric equations are
,
,
,
where and are parameters.
The parametric equations of a right cone with base radius and height are
,
,
,
where and are parameters.
The intersection curve of the two surfaces can be obtained by solving the system of three equations
for three of the four parameters . In this Demonstration, solving for , , and gives the parametric equations for the intersection curve with parameter (the curve consists of two parts, depending on the sign inside the equation for ):
,
,
,
with
and
.
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