6
QuizMultiple Choice

Conic Sections — Quiz

Question 6 • Precalculus

The angle between the generator and the central axis of a double-napped cone is 40 degrees A plane intersects the central axis at an angle between 40 degrees and 90 degrees Which conic section is formed?

Answer
A
parabola
B
hyperbola
C
circle
D
ellipse

Explanation

A plane parallel to a cone’s generator forms a parabola, which occurs when the angle between the plane and the axis equals the generator’s 40° angle. Here the plane’s angle with the axis is greater than 40° and less than 90°, so it cuts through only one nappe without being parallel to a generator. The resulting conic section is an ellipse.

AI-written and checked against the verified answer.

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