Lets examine different variations with
. The equation when a and k are
set at one, and 
is set at -2 
to 2 .
Now lets examine what happens when we vary a with the values (-2, -1, 1, and 2).
It would appear that changing a to a larger number increases the curve. Changing a to a negative value seems to produce the same circle only reflected over the y-axis.
If we now look at what happens if we put a back to one and vary k with the values -3,-2,-1,1,2, and 3.
If we look at what changed when k was one and negative one, we see that there appears to be no change, so one would guess that changing the k value to a negative would have no effect on the graph. We can come to a further conculsion by looking at when k is two and negative two. When k is two and negative two the graph that is produced is the same with four leaves and it does not seem to matter if it is positive or negative. This would further indicate that changing the k value to negatvie has no effect. This assumption can be again varified when looking at k is three and negative three. When k is three and negative three there are three leaves of the equations and nothing again seems to change.