Multiple Choice
How can you slice a vertically oriented 3D cone with a 2D plane to get a circle?
8. Conic Sections
Introduction to Conic Sections
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A vertically oriented 3D cone is sliced with a vertical 2D plane. What is the conic section that will form?
A
Circle:
B
Ellipse:
C
Parabola:
D
Hyperbola:
Verified step by step guidance1
Understand that a conic section is the intersection of a plane and a double-napped cone.
Identify the type of conic section formed by the intersection based on the angle and position of the plane relative to the cone.
A vertical plane slicing through a vertically oriented cone can produce different conic sections depending on the angle of the plane.
If the plane is parallel to the axis of the cone, the conic section formed is a hyperbola.
Therefore, when a vertical 2D plane slices a vertically oriented 3D cone, the conic section that forms is a hyperbola.
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