If a right circular cone intersects a plane that runs parallel to the cone's axis but does not pass through its vertex, the resulting curve is a pair of hyperboles.
If a right circular cone intersects a plane that runs perpendicular to the cone's axis but does not pass through its vertex the resulting curve will be a circle.
True.
circle
Hyperbola.
If a right circular cone intersects a plane that runs parallel to the edge of the cone the result curve will be a parabola, unless the intersection includes the vertex of the cone, in which case the intersection is a straight line. This is a conic section. Depending on the angle of the plane, the section will be a circle, an ellipse, a parabola, or two hyperboles.
hyperbola
parabola
parabola
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
If a right circular cone intersects a plane that runs perpendicular to the cone's axis but does not pass through its vertex the resulting curve will be a circle.
If a right circular cone intersects a plane that runs perpendicular to the cone's axis but does not pass through its vertex the resulting curve will be a circle.
The "conic section" that is produced when a right circular cone intersects a plane that runs parallel to the edge of the cone is a parabola. In the case where the plane also intersects the vertex of the cone, the parabola becomes two intersecting lines.
True
True.
Yes, it is true that if given a right circular cone a plane that intersects the cone not at the vertex and is parallel to its edge will always result in a parabola regardless of the shape of the cone. There are four cases... Plane perpendicular to axis: circlePlane between perpendicular to axis and parallel to edge: ellipsePlane parallel to edge: parabolaPlane between parallel to edge and parallel to axis: hyperbolehttp://en.wikipedia.org/wiki/Conic_section
The intersection of a right circular cone and a plane that is parallel to the edge of the cone is a parabola. However, if the vertex of the cone lies on the plane, then the intersection is simply two intersecting lines.
circle