Tilt of cutting plane is between (perpendicular to axis of the cone) and (parallel to the side of the cone).
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If it a right cone then it is a circle, otherwise an ellipse.
A conic section is a curve formed by the intersection of a plane with a cone (conical surface). If the section is parallel to the base of the cone, the conic section has a fixed diameter and is a circle. Any other plane that does not intersect the apex is either a parabola, a hyperbola, or an ellipse.
If a right circular cone intersects a plane that runs parallel to the edge of the cone the result curve will be a parabola, unless the intersection includes the vertex of the cone, in which case the intersection is a straight line. This is a conic section. Depending on the angle of the plane, the section will be a circle, an ellipse, a parabola, or two hyperboles.
The base of a cone is always a circle. it also can be a ellipse.
The hyperbola is the curve at the boundary of the intersection of the conewith a cutting plane parallel to the cone's axis.