Imagine a plane and a cone intersecting to form a parabola
b)Imagine the plane moving so that it keeps the same angle, but its point of intersection with the axis moves in the direction of the apex of the cone and eventually passes through the apex. Describe with happens to the parabola and write equations that describe how the parabola changes.

Question

Imagine a plane and a cone intersecting to form a parabola 
b)Imagine the plane moving so that it keeps the same angle, but its point of intersection with the axis moves in the direction of the apex of the cone and eventually passes through the apex. Describe with happens to the parabola and write equations that describe how the parabola changes.

ganeshie8 · Answer

Hey are you till stuck on this ?

shaeelynn · Answer

yes

ganeshie8 · Answer

I think the parabola degenerates to a point as the point if intersection approaches the apex

ganeshie8 · Answer

Let's try and put together some eqns

shaeelynn · Answer

okayy

thereisnousername · Answer

I think this video will be helpful. https://www.youtube.com/watch?v=HO2zAU3E... Don't worry about the angle stuff. You probably will never need to analyze conics with reference to the angle between the plane and the axis of the cone. Just pay attention to how the plane intersect the cone to give you a circle, ellipse, hyperbola, or parabola. It doesn't animate things to specifically answer your question, but it's close. Around 2:49 it discusses parabolas. Around 3:49 it discusses degenerate conics, where you get a point, line, or crossing lines. That does illustrate how the parabola gets so pointy , and gives you just a line. Hope that helps

shaeelynn · Answer

its says video does not exist

shaeelynn · Answer

@ganeshie8 can you please help??