Graphing 3D Equations: Solving x^2 + z^2 ≤ 9

[Miike012]

I am having difficulty graphing equatioins in 3D for instance...

what does the graph in 3-D look like x^2 + z^2 ≤ 9?

Apparently its a cylinder extending along the y-axis. My initial guess was it was a 2-D circle with radius 3 on the xz plane. Anyways how should I have known it extended along the y-axis?

 

[Mark44]

I am having difficulty graphing equatioins in 3D for instance...

what does the graph in 3-D look like x^2 + z^2 ≤ 9?

Apparently its a cylinder extending along the y-axis. My initial guess was it was a 2-D circle with radius 3 on the xz plane. Anyways how should I have known it extended along the y-axis?

The statement of the problem probably says something about graphing the set of points (x, y, z) such that x² + z² ≤ 9.

Since the inequality doesn't include a y term, the y coordinates are completely arbitrary. That's why the graph extends along the y-axis.

 

[Miike012]

Another question... the 3d picture is on the paint doc and I am wondering why the entire surface is only in the first octant because isn't the point (which I hightligted in the paint document) in the 3rd octant?

 

[Mark44]

That graph is screwy.

The graph of the equation z = 2x² + 2y² - 4 is a paraboloid that opens up from its vertex at (0, 0, -4), and whose central axis lies along the z-axis. In your picture, the thing appears to be in the first octant.

 

[LCKurtz]

Another question... the 3d picture is on the paint doc and I am wondering why the entire surface is only in the first octant because isn't the point (which I hightligted in the paint document) in the 3rd octant?

It isn't in the first octant. It is correct. The planes that look like the coordinate planes aren't $x=0$ and $y=0$. Look how the axes are labeled.

 

[Mark44]

It isn't in the first octant. It is correct. The planes that look like the coordinate planes aren't $x=0$ and $y=0$. Look how the axes are labeled.

Good point. I saw how the axes are labeled, but I didn't notice that the planes you see aren't the regular coordinate planes.