170840
AssignmentMultiple Choice

Conic Sections

Question 170840 • Precalculus

What describes θ when an ellipse is created from an intersection of a plane and double-napped cone?

Answer
A
θ = α
B
θ = 90⁰
C
α < θ < 90⁰
D
0⁰ ≤ θ < α

Explanation

For an ellipse, the cutting plane must intersect only one nappe of the cone and must not be parallel to a generator. If θ is the angle between the plane and the cone’s axis, this means it lies between the cone’s half-angle α and 90°: α < θ < 90°. Thus, the correct choice is “α < θ < 90°.”

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