Two possible shapes are ...
1. point - slicing the cone at its apex, perpendicular to the axis of symmetry (degenerate circle)
2. 2 intersecting lines - slicing the cone on its axis of symmetry (degenerate hyperbola)
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More conventional cross sections include a circle (⊥ to axis), ellipse (between ⊥ to axis and parallel to side), parabola (parallel to side), hyperbola (oblique to side up to and including parallel to axis), line (tangent to side).