SOLUTION: if a right circular cone intersects a plane that goes through both nappes of the cone, but not through the vertex, the resulting curve will be an

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Question 737426: if a right circular cone intersects a plane that goes through both nappes of the cone, but not through the vertex, the resulting curve will be an
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

If the angle of the plane is less than the angle of the cone, then the intersection is a point.
If the angle of the plane is greater than the angle of the cone, then the intersection is two+lines intersecting at the vertex.
If the plane insersects at other than the vertex, then the intersection is a circle when the plane is perpendicular to the cone's axis, an ellipse when the plane's angle is less than the cone's angle, a parabola when the planes's angle equals the cone's angle, and two hyperbola's in the last case.
If a right circular cone is intersected by a plane so that the intersection goes through the cone's vertex as well as an edge of each nappe, the shape produced is a line.
in your case, if a right circular cone intersects a plane that goes through both nappes of the cone, but not through the vertex, the resulting curve will be a hyperbola