Question

question 8 of 10

given a right circular cone, a plane that intersects the cone (not at the vertex) and is parallel to its edge will always result in a parabola, regardless of the shape of the cone.

a. true
b. false

Explanation:

Analyze the geometric definition of a parabola as a conic section

A parabola is formed by the intersection of a right circular cone and a plane that is parallel to a generating line (the slant edge or generator) of the cone.

Evaluate the conditions given in the statement

The statement specifies:

1. A right circular cone.
2. A plane intersecting the cone (not at the vertex).
3. The plane is parallel to its edge (generator).

These conditions precisely define the geometric construction of a parabola, which holds true regardless of the specific dimensions (aperture or shape) of the right circular cone.

Determine the truth value

Since the geometric definition is satisfied under all given conditions, the statement is true.

Answer:

• A. True (Correct answer)
• B. False