A parabola.
Then the cross-section is a circle or a point.
Hyperbola
A 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.
A cylinder has a circular cross section that is parallel to its base.
Then the cross-section is a circle or a point.
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.
Hyperbola
A 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.
A cylinder has a circular cross section that is parallel to its base.
If your question is "What is the cross-section of the intersection?" then the answer is "A circle." Otherwise, I can't make sense of the question.
The answer depends on the angle at which the axis of the cone intersects the cross-sections.
The question is incomplete, because "the following" was not provided. A circle, however, is a conic section where the sectioning plane is perpendicular to the cone's axis of symmetry and intersects each generator or, more specifically, if it is not a right circular cone, parallel to the generating circle of the cone.
It is a section of a right circular cone by a plane that is parallel to one generating line of the cone.
The vertical cross section of a cylinder is a rectangle. It is created by slicing the cylinder along a plane parallel to its base. The resulting shape will have the same height as the cylinder but a width equal to the diameter of the base.
A circular section refers to a part or segment of a larger circular object or shape. It typically describes a section that is formed by cutting or dividing the circular object along a specific path or line. The circular section retains the characteristics and properties of the original circular shape.