5
QuizMultiple Choice

Equations of Ellipses

Question 5 • MO-Algebra II A-CR

The angle between the generator and the central axis of a double-napped cone is 60°. A plane intersecting the cone makes an angle of 50° with the central axis. Which conic section is formed?

Answer
A
circle
B
ellipse
C
hyperbola
D
parabola

Explanation

The cone’s generator makes a 60° angle with its axis, while the plane makes a 50° angle with the axis. Because 50° is less than 60°, the plane is tilted enough to intersect both nappes of the double cone, forming a hyperbola. The correct choice is hyperbola.

AI-written and checked against the verified answer.

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