If both nappes of a right circular cone are intersected by a plane that does not pass through the vertex of the cone, the resulting curve will be a(n) _____.A.circleB.parabolaC.hyperbolaD.ellipse
Question
If both nappes of a right circular cone are intersected by a plane that does not pass through the vertex of the cone, the resulting curve will be a(n) _____.A.circleB.parabolaC.hyperbolaD.ellipse
Solution
The answer is D. ellipse.
Here's why:
A right circular cone has a point, known as the vertex, from which straight lines (generators) extend to form a curved surface. The nappes of a cone are the two halves of the cone on either side of the vertex.
When a plane intersects both nappes of a right circular cone but does not pass through the vertex, it cuts through the cone in two places. The intersection of the plane and the cone forms a closed curve on each nappe. These curves are identical and symmetrical to each other, and they are known as ellipses.
Therefore, the resulting curve when a plane that does not pass through the vertex intersects both nappes of a right circular cone is an ellipse.
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