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.hyperbolaC.ellipseD.parabola
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.hyperbolaC.ellipseD.parabola
Solution
The answer is C. ellipse.
Here's why:
A right circular cone has a point, known as the vertex, from which straight lines (generators) extend to form a circular base. This cone has two parts or 'nappes', one above and one below the vertex.
When a plane cuts through both nappes of the cone but does not pass through the vertex, it creates two intersecting curves. These curves form an ellipse, which is a closed curve where the sum of the distances from any point on the curve to two fixed points (the foci) is constant.
So, the resulting curve from such an intersection would be an ellipse.
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