Which intersection forms a parabola?

1.) A plane intersects only one nappe of a double-napped cone, and the plane is parallel to the generating line of the cone.

2.) A plane intersects both nappes of a double-napped cone, and the plane does not intersect the vertex.

3.) A plane intersects only one nappe of a double-napped cone, and the plane is not parallel to the generating line of the cone.

4.) A plane intersects only one nappe of a double-napped cone, and the plane is perpendicular to the axis of the cone.

Gwendolynkristine
May 5, 2017

#1**+2 **

Which intersection forms a parabola?

1.) A plane intersects only one nappe of a double-napped cone, and the plane is parallel to the generating line of the cone. Umm What is the generating line of a cone? idk

a generator is a (any) straight line which runs from the apex of the cone to the base

Yep it must be this one becasue the plane has to inersect with the base of the cone.

This is really confusing though ://

2.) A plane intersects both nappes of a double-napped cone, and the plane does not intersect the vertex. Nope - not this one! That would be hyperbola

3.) A plane intersects only one nappe of a double-napped cone, and the plane is not parallel to the generating line of the cone. This would be an ellipse!

4.) A plane intersects only one nappe of a double-napped cone, and the plane is perpendicular to the axis of the cone. No that would be the circle

the answer is provided in the site that I have referenced below :)

Reference: http://www3.ul.ie/~rynnet/swconics/planes_cutting_coneA.htm

It says:

THE PARABOLA

The section is a parabola when the plane is parallel to a generator, and only one of the cone.

Melody
May 6, 2017