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.
circle
True.
Hyperbola.
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 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.
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.
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.
hyperbola
circle
parabola
circle
True
True.
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.