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If a right circular cone is intersected by a plane so that the intersection goes through the cone's vertex as well as an edge of each nappe, the shape produced is a line.

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If the angle of the plane is less than the angle of the cone, then the intersection is a point. If the angle of the plane is greater than the angle of the cone, then the intersection is two lines intersecting at the vertex.

If the plane insersects at other than the vertex, then the intersection is a circle when the plane is perpendicular to the cone's axis, an ellipse when the plane's angle is less than the cone's angle, a parabola when the planes's angle equals the cone's angle, and two hyperbole's in the last case.

Q: If a right circular cone is intersected by a plane so that the intersection goes through the cone's vertex as well as an edge of each nappe what shape is produced?

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Continue Learning about Other Math

A line is produced

if a right circular cone intersects a plane that goes through both nappes of the cone, but not through the vertex, the resulting curve will be a hyperbola

If all three lines are parallel, there are zero points of intersection. If all three lines go through a point, there is one point of intersection. If two lines are parallel and the third one crosses them, there are two. If the three lines make a triangle, there are three points.

Rotation.

If it's parallel to the base, it's a circle. If it doesn't go through the base, it's an ellipse. If it's does, it's hyperbolic/parabolic.

Related questions

If I understand your description correctly, a line.

A line is produced

An Ellipse

An ellipse is produced.

It will be a hyperbola.

hyperbola

hyperbola

The intersection forms a hyperbola.

Then the intersection is a hyperbola.

CIRCULAR

When it is produced it is processed through a tube, giving it a circular shape.

A steady circular yellow light on a traffic signal indicates that the signal is about to change to red. Drivers should prepare to stop safely before the intersection if it is safe to do so.