Question

if a right circular cone is intersected by a plane only at its vertex, as in the picture below, what shape is produced?

a. a point
b. a line
c. a circle
d. a hyperbola
e. a parabola

Explanation:

Analyze the intersection of the plane and the cone

The problem asks for the shape produced when a plane intersects a double right circular cone only at its vertex.

Identify the resulting geometric shape

Since the plane passes through the vertex and does not intersect any other part of either the upper or lower cone, the only point of intersection between the plane and the double cone is the single point at the vertex. This is a degenerate conic section known as a point.

Answer:

• A. A point (Correct answer)
• B. A line
• C. A circle
• D. A hyperbola
• E. A parabola