[math-fun] Circle question

Consider a circle whose diameter lies on a fixed axis line passing obliquely through a plane (not perpendicular to the plane) Now rotate the circle about the axis line subject to the following conditions: - The plane position is fixed. - The circle radius is fixed. - The axis is parallel to its initial position. - The circle is tangent to the plane, on the same side of the plane as its initial position. Can the circle be made to move without slippage along the plane? What is the locus of the point of circle-plane contact?