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.ellipseB.circleC.parabolaD.hyperbolaSUBMITarrow_backPREVIOUS
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.ellipseB.circleC.parabolaD.hyperbolaSUBMITarrow_backPREVIOUS
Solution
The answer is B. circle.
Here's why:
A right circular cone has a circular base and a vertex that is not on the base. The nappes of a cone are the two halves of the cone on either side of the vertex.
If a plane intersects both nappes of the cone but does not pass through the vertex, it will cut out two circles on the cone. This is because the intersection of a plane with a cone is a conic section, and in this case, the conic section is a circle.
So, the resulting curve will be a circle.
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