What is the intersection of a cone and a plane parallel to a line along the side of the cone?
Provide mathematical examples to support your opinions. You may use equations, diagrams, or graphs to organize and present your thoughts.

Question

What is the intersection of a cone and a plane parallel to a line along the side of the cone?  
Provide mathematical examples to support your opinions. You may use equations, diagrams, or graphs to organize and present your thoughts.

e.mccormick · Answer

Famillior with your conic sections?  Know what the whole group is?

anonymous · Answer

no

jim_thompson5910 · Answer

This page may help http://math2.org/math/algebra/conics.htm If not, let me know

anonymous · Answer

that doesn't even look like English.

e.mccormick · Answer

OK.  Yah, Jim posted a good link.

There is a set of equations for the circle, ellipse, hyerbola, and parabola.  They call these collectively the conic sections.

anonymous · Answer

okay..

e.mccormick · Answer

If you look at the upper left picture, you can see the faded gray plane slicing through the hourglass, which is just a pair of cones.  Where they intersect, it makes a circle.  So the plane has cut a curcular section in the cone.

anonymous · Answer

okay.

e.mccormick · Answer

For the ellipse, the plane is at an angle.  Again, ghr section it cuts or intersection is where they get the name conic sections.

e.mccormick · Answer

ght... the...  ignore poor typing... =P

anonymous · Answer

ok.

e.mccormick · Answer

Now, on your problem, it says parallel to the line of the cone, I bet that part is a little confusing.  Right?

anonymous · Answer

all of it is confusing.

e.mccormick · Answer

OK.  Well, you know what parallel is, so lets start with some lines.|dw:1366509573056:dw|So parallel lines, right?  Simple enough so far.

anonymous · Answer

yes.

e.mccormick · Answer

|dw:1366509629829:dw|So now I have added the rest of the cone and the plane parallel to it.  The intersection is what we are looking at as the answer.