**The first equation we graph is**

**To see the steps to rewrite this polar equation
in rectangular form, ****click here.**

**The second equation of interest at this
moment is**

**We expect from the equation that the first
equation is the parent of this one and that the graph will reflect
this relationship.**

**Indeed, the new graph closely resembles
the first graph. The difference between the graphs being that
this one is rotated 45 degrees counterclockwise about the origin,
as seen here (red = original).**

**To view further rotations of the original
graph, ****click here. **

**The final equation we will investigate is**

**Let's see what happens when we change individual
signs within the equation. ****Click here.**