Intro to 3D Equations

What is the equation of the xy-plane in the Three Dimensional Space? What about the zy-plane?

What does the graph of x=2 look like when viewed on a number line (Singular Dimension)?

What does the graph of x=2 look like when viewed in the 2 Dimensional Cartesian plane?

What does the graph of x=2 look like when viewed in 3 dimensions?

1. What’s the equation of a plane parallel to the xy-plane and contains the point (3, 4, 8)?
2. What’s the equation of a plane parallel to the xz-plane and contains the point (1, 6, 5)?
3. What's the equation of a plane perpendicular to the yz-plane and contains the point (1, 6, 5)
4. What's the equation of a plane perpendicular to the xz-plane and contains the point (1, 6, 5)?

What does the graph of look like when viewed in the Cartesian plane?

Describe the graph of in the Cartesian Plane.

The last two graphs you described are created in the Cartesian plane, in other words, they are 2-dimensional. What do the same graphs look like when examined in 3 dimensions? Make your conjectures and test them using the applet below.

Describe the intersection of and .

Describe the graph of each of the following

Find the equation(s) for a circle with radius 3 centered at and lying in a plane parallel to the yz-plane.

Find the equation(s) of a with radius 2 centered at and lying in a plane perpendicular to the xz-plane.