Question

which conic section results from the intersection of the plane and the double - napped cone shown in the figure?

ellipse
circle
parabola
hyperbola

Explanation:

• Ellipse: Formed when a plane intersects a cone at an angle (not parallel to the side of the cone and not perpendicular to the axis).
• Circle: A special case of an ellipse where the plane is perpendicular to the axis of the cone.
• Parabola: Formed when the plane is parallel to the side of the cone.
• Hyperbola: Formed when the plane intersects both nappes of the double - napped cone.

In the given figure, the plane intersects only one nappe of the double - napped cone and is parallel to the side of the cone.

Answer:

parabola