Am i correct?
A plane intersects only one nappe of a double-napped cone. It is neither perpendicular to the cone's axis nor parallel to its generating line. Which conic section is formed?
point
circle
ellipse <---
parabola
correct
thank you, Steve :)
Yes, you are correct. The conic section that is formed when a plane intersects only one nappe of a double-napped cone, and is neither perpendicular to the cone's axis nor parallel to its generating line, is an ellipse.
To understand why this is the case, it helps to visualize the different possibilities of the plane's intersection with the cone.
If the plane is perpendicular to the cone's axis, the intersection will result in a circle. This is because the plane cuts through both nappes of the cone symmetrically at equal distances from the vertex.
If the plane is parallel to the generating line of the cone, the intersection will be a parabola. This is because the plane intersects only one nappe of the cone, extending infinitely in one direction.
In the scenario you described, where the plane intersects only one nappe but is neither parallel to the generating line nor perpendicular to the cone's axis, the result is an ellipse. This is because the intersection creates a closed curve that is symmetric about both the x and y-axes, resembling an elongated circle.
Therefore, the correct conic section in this case is an ellipse.