By Alicia Rosenberger
Let's investigate:
How will these formulas look? are they similar?
First let's take a look at
the graph looks like,
Next, let's take a look at
whose graph looks like:
We see some similarities here between the first and second graphs. They are both polar equations of ellipses. The difference between the first and second graph is that the second graph is similar to the first one except it is at an angle. We see this has something to do with the subrtraction of 
from theta. This subtraction is what gives the oval shape its diagonal looking angle.
the third one,
looks like:
The third graph differs from the first two because it is a polar form of an equation like f(x)/g(x). We see where the graph jumps at x=-2. This graph is different because it is defined at all values of x except -2, and it is defined for all values of y except -2. The graph will forever approach -2 but will never reach -2. Whereas in the first graph, x ranges from -2 to 8, and y ranges from -4 to 4. In the scond graph we see x ranges from -3 to 7 and y ranges from -3 to 7 as well.