The intersection of a plane with a right circular could be...

The intersection of a plane with a right circular could be which of
the following?
I. A circle
II. Parallel lines
III. Intersecting lines
(A) I only
(B) II only
(C) III only
(D) I and II only
(E) I, II, and III

Labs

Want to see this concept in action?

NEW

Explore this concept interactively to see how it behaves as you change inputs.

View Labs

Key Concepts

Conic Sections

Conic sections are the curves obtained by intersecting a plane with a double right circular cone. Depending on the angle at which the plane intersects the cone, the resulting curves can be a circle, ellipse, parabola, or hyperbola, or degenerate cases such as a point, a line, or a pair of intersecting or parallel lines.

Intersection of a Plane and a Cone

The intersection of a plane with a cone involves positioning the plane in various ways relative to the cone's axis and vertex. This relative orientation determines whether the resulting curve is a non-degenerate conic (such as a circle, ellipse, parabola, or hyperbola) or a degenerate one (such as intersecting lines or parallel lines).

Degenerate Conic Sections

Degenerate conic sections occur when the intersecting plane cuts through the cone in special ways, often involving the vertex of the cone. In these cases, instead of a smooth curve, the intersection may form simpler geometric figures like a single line, a point, a pair of intersecting lines, or even two parallel lines, each representing limits or special instances of the general conic sections.

Transcript

Please give Ace some feedback