A parabola.
Then the cross-section is a circle or a point.
Hyperbola
A hyperbola.
Shapes that have a circular cross-section include cylinders, spheres, and cones. In a cylinder, each cross-section parallel to the base is a circle, while a sphere has circular cross-sections at any plane that intersects it. A cone also has circular cross-sections parallel to its base, becoming smaller as it approaches the apex.
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.
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.
Shapes that have a circular cross-section include cylinders, spheres, and cones. In a cylinder, each cross-section parallel to the base is a circle, while a sphere has circular cross-sections at any plane that intersects it. A cone also has circular cross-sections parallel to its base, becoming smaller as it approaches the apex.
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 2D parallel shape that represents a cross section of a cylinder is a circle. When a cylinder is sliced parallel to its base, each cross section reveals a circular shape, regardless of where the cut is made along the height of the cylinder. This circular cross section maintains the same diameter as the bases of the cylinder.
A cone can be divided into two main sections when cut by a plane: a circular base and a curved surface. If the plane intersects the cone parallel to the base, it creates a circular section called a cross-section. Additionally, if the cone is sliced vertically, it can produce triangular sections depending on the angle of the cut. Overall, the cone can be analyzed in terms of its base, curved surface, and various cross-sections depending on the type of cuts made.
A horizontal cross section of a cylinder results in a circle. This is because when you slice horizontally through the cylinder, each cut intersects the circular bases, producing a circular shape. The radius of the circle corresponds to the radius of the cylinder.