Which term best describes the point, line, or curve defined by the intersection of a cone and a plane?A.Planar sectionB.Conic sectionC.Conic lineD.Planar line
Question
Which term best describes the point, line, or curve defined by the intersection of a cone and a plane?
A. Planar section
B. Conic section
C. Conic line
D. Planar line
Solution
The term that best describes the point, line, or curve defined by the intersection of a cone and a plane is B. Conic section.
A conic section is formed when a plane intersects a cone. Depending on the angle of the intersection, this can yield different types of curves, such as:
- A circle (when the plane is perpendicular to the axis of the cone)
- An ellipse (when the plane intersects the cone at an angle, but does not pass through the base)
- A parabola (when the plane is parallel to the edge of the cone)
- A hyperbola (when the plane intersects both halves of the cone)
Thus, in the context of the definitions provided, "Conic section" accurately captures the concept of what is formed through that intersection.
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