Intersecting a Rotating Cone with a Plane

angle

height

If the center of the cone is in the plane, the intersection is a point, a straight line, or a pair of straight lines, depending on the angle of the axis of the cone.

If the center of the cone is not in the plane, the intersection is a conic section. Let

v

be the angle of the cone, that is, the angle between the axis and one of the generating lines of the cone. You get a circle if the angle is

0

or

π

, an ellipse if the angle is between

0

and

π-v

(or between

π+v

and

2π

), a parabola if the angle is

π±v

, and a hyperbola if the angle is within

v

of

π

.

External Links

Line-Plane Intersection (Wolfram MathWorld)

Cone (Wolfram MathWorld)

Circle (Wolfram MathWorld)

Ellipse (Wolfram MathWorld)

Parabola (Wolfram MathWorld)

Hyperbola (Wolfram MathWorld)

Conic Section (Wolfram MathWorld)

Permanent Citation

George Beck

"Intersecting a Rotating Cone with a Plane"
http://demonstrations.wolfram.com/IntersectingARotatingConeWithAPlane/
Wolfram Demonstrations Project
Published: September 28, 2007