Question

question 5 of 10

if both nappes of a right circular cone are intersected by a plane that does not pass through the vertex of the cone, the resulting curve will be a(n) ______.

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

Explanation:

Analyze the intersection of a plane with a double-napped cone

A right circular cone consists of two parts, known as nappes, which meet at the vertex. When a plane intersects both nappes of the cone without passing through the vertex, it cuts through both the upper and lower cones.

Identify the resulting conic section

An intersection that cuts through both nappes of a double cone creates a curve with two separate, open branches. By definition, this geometric curve is a hyperbola.

Answer:

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