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The intersection of a right circular cone and a plane that is parallel to the edge of the cone is a parabola. However, if the vertex of the cone lies on the plane, then the intersection is simply two intersecting lines.
No. If they are parallel, then a plane exists which both lines lie in. Skew lines can not be on the same plane.
the lines are parallel.
Parallel lines Never Converge
skew lines are noncoplanar lines, which means they aren't parallel and they also don't intersect skew lines do not intersect and are not coplanar