A parabola is the figure formed by the intersection of a circular cone and a plane that lies parallel to the edge of the cone. (the cone does not have to be a right [90°] circular cone).
If this is a homework question, please consider trying to answer it yourself first, otherwise the value the reinforcement of the lesson by doing the homework will be lost to you.If plane intersects a right circular cone perpendicular to the axis of the cone then the shape of the 2 dimensional figure formed from the intersection of the plane with the cone is a circle. At the vertex of the cone, the circle becomes a point. In the general case of any plane intersecting any cone, the intersection is known as a conic section.
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 cone's axis but does not pass through its vertex, the resulting curve is a pair of hyperboles.
Then the intersection is a 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.
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.
I'm assuming you are looking for the name of the conic section produced by this type of intersection? If a right circular cone is intersected by a plane parallel to one edge of the cone, the resulting curve of intersection would be a parabola. If the intersecting plane was parallel to the base, it would be a circle. If the intersecting plane was at any angle between being parallel to the base and being parallel to an edge, it would produce an ellipse or part of an ellipse (depending on whether the intersection was completely within the cone).
A parabola is the figure formed by the intersection of a circular cone and a plane that lies parallel to the edge of the cone. (the cone does not have to be a right [90°] circular cone).
If this is a homework question, please consider trying to answer it yourself first, otherwise the value the reinforcement of the lesson by doing the homework will be lost to you.If plane intersects a right circular cone perpendicular to the axis of the cone then the shape of the 2 dimensional figure formed from the intersection of the plane with the cone is a circle. At the vertex of the cone, the circle becomes a point. In the general case of any plane intersecting any cone, the intersection is known as a conic section.
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 cone's axis but does not pass through its vertex, the resulting curve is a pair of hyperboles.
Helix
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 it is a right circular cone, it has an infinite number of planes of symmetry. If it is an oblique circular cone, it has one plane of symmetry.
Then the intersection is 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.