Question

a(n) _____ is produced when you slice a cone with a plane that passes through only one nappe of the cone but is not parallel to an edge of the cone.

a. circle
b. hyperbola
c. ellipse
d. parabola

Explanation:

Analyze the geometric conditions of the conic section slice

• The slicing plane passes through only one nappe of the double cone.
• The slicing plane is not parallel to an edge (generator) of the cone.
• A plane parallel to the edge of the cone intersecting one nappe produces a parabola.
• A plane perpendicular to the axis of the cone produces a circle.
• A plane tilted such that it cuts through only one nappe entirely (and is not parallel to the edge) produces an ellipse.
• A plane intersecting both nappes produces a hyperbola.

Match the conditions to the correct conic section

• Since the plane cuts through only one nappe and is not parallel to the edge, the resulting cross-section is an ellipse.

Answer:

• A. circle
• B. hyperbola
• C. ellipse (Correct answer)
• D. parabola