Three Dimensional Space

1. Consider the set of points $(x,y,z)$ that satisfy the equation $x=2$. Write a sentence to describe this set as best as you can.

2. Consider the set of points $(x,y,z)$ that satisfy the equation $y=-1$. Write a sentence to describe this set as best as you can.

3. Consider the set of points $(x,y,z)$ that satisfy the equation $z=0$. Write a sentence to describe this set as best as you can.

In this exercise, we want to algebraically identify when the graph of a given equation can be expressed as:

• $y$ as a function of $x$, but $x$ cannot be written as a function of $y$
• $x$ as a function of $y$, but $y$ cannot be written as a function of $x$
• $y$ as a function of $x$ and $x$ as a function of $y$
• neither $y$ as a function of $x$ nor $x$ as a function of $y$

For each equation below, state which of the four options above appl…

Find the equation of each of the following geometric objects.

1. The plane parallel to the $xy$-plane that passes through the point $(-4,5,-12)$.

2. The plane parallel to the $yz$-plane that passes through the point $(7, -2, -3)$.

3. The sphere centered at the point $(2,1,3)$ and has the point $(-1,0,-1)$ on its surface.

4. The sphere whose diameter has endpoints $(-3,1,-5)$ and $(7,9,-1)$.