In order to continue enjoying our site, we ask that you confirm your identity as a human. Thank you very much for your cooperation.
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: //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.
KaerylleAmethyst KaerylleAmethyst
A conic section (or simply conic) is a curve obtained as the intersection of the surface of a cone with a plane. The three types of conic sections are the hyperbola, the parabola, and the ellipse. ... If the plane intersects one nappe at an angle to the axis (other than 90∘ ), then the conic section is an ellipse.
--C.Ellipse
-
Thanks! But is this sure?
-