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.
ellipse
The intersection of the cone and that particular plane is a parabola.
Then the intersection is a hyperbola.
hyperbola
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 parallel to the cone's axis but does not pass through its vertex, the resulting curve is a pair of hyperboles.
A Parabola.
ellipse
Parabola
The intersection of the cone and that particular plane is a parabola.
Then the intersection is a hyperbola.
hyperbola
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.
If a right circular cone intersects a plane that passes through one of its nappes, but the plane is not parallel to an edge of the cone, the resulting curve will bea(n) _____ . ellipse
A parabola.
hyperbola