The intersection of the cone and that particular plane is a parabola.
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.
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.
Then the cross-section is a circle or a point.
True.
ellipse
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.
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
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
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.
Then the cross-section is a circle or a point.
True.
A Parabola.
Parabola
ellipse
Then the intersection is a hyperbola.
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