Question

What is the common set of points for these figures called—an intersection or a crosssection? Place a check mark by the correct name. Describe the geometric figure formed by the common points. Assume that the two figures have more than one point in common.

A circle and the lateral surface of a cone.
a- Cross section
b-Intersection
Figure formed:

Answer 1

The common set of points when a circle intersects the lateral surface of a cone is called an intersection, and the shape formed is a conic section, which can be a circle or an ellipse depending on the angle of intersection.

Step-by-step explanation:

The common set of points for a circle and the lateral surface of a cone when they intersect is called an intersection. If we assume that these two figures have more than one point in common and the circle is in a plane that cuts through the cone's lateral surface, the shape of the intersection would likely be a conic section.

The type of conic section formed depends on the angle at which the plane intersects the cone's surface.

If the plane cuts perpendicular to the cone's axis, the intersection will be a circle. If the plane cuts at an oblique angle, the intersection might be an ellipse. However, without specific information about the angle of the intersection, we can simply say that the figure formed is a conic section.