1. ## surfaces and solids

Hello people,

I am finding it hard to recognize the difference between paraboloids,cylinders,cones and etc..(any 3d surfac)
How do I tell the difference between them?
for example y^2+4z^2=9 where does this curve open up..how do i tell?
I know I am asking stupid questions ..
thanks

2. ## Re: surfaces and solids

That will be an ellipse on the plane x = 0. Do you see that it is a 2D curve since there are only 2 variables?

3. ## Re: surfaces and solids

Originally Posted by MarkFL
That will be an ellipse on the plane x = 0. Do you see that it is a 2D curve since there are only 2 variables?
wrong aproach...............see the figure below.

4. ## Re: surfaces and solids

Originally Posted by MarkFL
That will be an ellipse on the plane x = 0. Do you see that it is a 2D curve since there are only 2 variables?
There are only two variables in this equation- that does not necessarily mean that we are to assume only two dimensions. If we are given that this is a 3D situation then it is "y^2+ 4z^2= 9 for all x" and is an elliptic cylinder whose axis is the x-axis.