What is the shape of the cross-section, when a cone is cut by a plane parallel to its slant height?

The intersection of a right circular cone with a plane creates different geometric curves called conic sections:
1. Circle: Formed when the cutting plane is perpendicular to the central axis of the cone.
2. Ellipse: Formed when the plane is slightly tilted but cuts completely through one nappe of the cone.
3. Parabola: Formed when the cutting plane is perfectly parallel to the slant height (generator line) of the cone.
4. Hyperbola: Formed when the plane is parallel to the central axis or cuts through both nappes of the cone.

Thus, a plane parallel to the slant height yields a Parabola.