Thread: Surfaces

Consider the following surface:

x = 4y^2 + 4z^2

What's this surface called?

What coordinate plane does z=0 define?

What's the trace of this surface in the xz plane look like?

What's the trace of this surface in the planes x=k look like?

Originally Posted by Ideasman

Consider the following surface:

x = 4y^2 + 4z^2

What's this surface called?
What coordinate plane does z=0 define?
What's the trace of this surface in the xz plane look like?
What's the trace of this surface in the planes x=k look like?

Hello,

I've attached a diagram of this surface.

a) It is a rotation paraboloid. The axis of rotation is the positive x-axis.

b) It's a parabola with the vertex in the origin:

c) It's a circle:

EB

Hello, Ideasman!

I use the standard orientation of the three coordinate axes.

Code:

                  z
                  |
                  |
                  |
                  |
                  * - - - - - - y
                /
              /
            /
          x

Consider the following surface: .

What's this surface called?

It is a paraboloid.

What coordinate plane does define?

is the -plane (the "floor" of the graph).

What's the trace of this surface in the -plane look like?

The -plane is the "left wall" of the graph.

Let and we have: .

This is a parabola on the "left wall", vertex at the origin,
. . opening in the positive -direction.

What's the trace of this surface in the planes look like?

Let . .We have: .

These are circles: centered on the -axis with radius