Curve of intersection — When a plane cuts a circular cylinder (not a cone), is the resulting curve correctly named a “conic section,” or should it be described simply as an ellipse/circle produced by a plane–cylinder cut?

Introduction / Context:
In descriptive geometry, the names of intersection curves matter for precision. “Conic section” has a specific classical meaning: the locus obtained when a plane intersects a cone. A plane intersecting a cylinder can produce a circle or an ellipse, but the naming convention differs from the conic-section definition.

Given Data / Assumptions:

• The statement claims the plane–cylinder intersection is “called a conic section.”
• We consider a circular right cylinder cut by an arbitrary plane.
• The observed curve may be a circle (if cut perpendicular to axis) or an ellipse (if cut obliquely but not parallel to generators).

Concept / Approach:
Although the resulting ellipse is the same geometric shape as one conic type, the term “conic section” refers historically and definitionally to plane–cone intersections. For clarity in drafting/teaching, we typically say “ellipse obtained by cutting a cylinder.” Calling it a conic section blurs the standard classification and source geometry used in many textbooks and standards.

Step-by-Step Solution:
1) Recall definition: conic sections arise from plane–cone intersections (circle, ellipse, parabola, hyperbola).2) Recognize the scenario: plane–cylinder intersection produces a circle or ellipse.3) Naming: describe it as “ellipse (or circle) from plane–cylinder intersection,” not a conic section.

Verification / Alternative check:
Constructive proofs in descriptive geometry derive cylinder–plane ellipses using auxiliary views without invoking cone geometry; pattern development texts maintain the naming distinction for pedagogical consistency.

Why Other Options Are Wrong:

• Correct: Overextends the term “conic section.”
• Projection-dependent options: The nature of the curve does not depend on orthographic vs pictorial projection.
• “Depends on obliquity”: Obliquity changes whether the curve is a circle or ellipse, not the classification as a conic section.

Common Pitfalls:
Assuming any ellipse must be a “conic section” by name; forgetting that definitions link shapes to generating solids; mixing classification with visual appearance.

Final Answer:
Incorrect