Question

a plane intersects the vertex of the cone.
a plane intersects the edge of the cone.
a plane intersects only one nappe of the cone parallel to a base of the cone.
a plane intersects only one nappe of the cone and is not parallel to any part of the cone.
a plane cuts through both nappes of the cone, but not through the cones vertex.
a plane cuts through only one nappe of the cone parallel to an edge of the cone.

1. draw a line on each cone to show how a plane could intersect the cone to form the conic section written above it.

ellipse
hyperbola
circle
line
parabola

Explanation:

Step1: Recall conic - section definitions

Conic sections are formed by the intersection of a plane and a cone. Different intersections result in different conic - sections.

Step2: Match intersection descriptions with conic - sections

• When a plane intersects the vertex of the cone, the result is a point, a line, or a pair of intersecting lines. In the context of the given options, it corresponds to a line.
• When a plane intersects the edge of the cone, the result is a line.
• When a plane intersects only one nappe of the cone parallel to a base of the cone, the result is a circle.
• When a plane intersects only one nappe of the cone and is not parallel to any part of the cone, the result is an ellipse.
• When a plane cuts through both nappes of the cone, but not through the cone's vertex, the result is a hyperbola.
• When a plane cuts through only one nappe of the cone parallel to an edge of the cone, the result is a parabola.

Answer:

1. Line
2. Line
3. Circle
4. Ellipse
5. Hyperbola
6. Parabola