Abstract: A left and a right spacial intersection curves are formed by a cylinder and a cone with their axes intersected. The research is focused on the left intersection curve, and the variation rule of its ultra right point is derived using mathematical method as the radius of the cylinder varying. Then a graphical method to draw the exact position of the ultra right point on the left intersection curve is provided. The ultra right point of the left intersection curve is on two particular intersection curves, namely, the intersection curve of the cone and its tangent sphere and the intersection curve of the cylinder and the sphere mentioned above.

Key words: engineering graphics, descriptive geometry, intersection curve, analytical proof, graphical method