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.