A right circular cone is intersected by a plane that passes through only one nappe of the cone and is parallel to an edge of the cone, as in the pictire below. What object is produced from this intersection?

Parabola

It's not always easy to visualize this stuff. Do a Google image search for "3D Conic Sections" and take a look at a bunch of the results. That may help a bit. Let me know if you have any other questions.