__What happens when a = 0?__

If a = 0 and k = 1, the equation will graph as a circle with a diameter of b.

If you click on the following link, you will see an animation of y = bcosq for values of b such that -3 < x < 3.

If a = 0 and k is a nonzero integer, then the equation will graph as a rose where b represents the maximum distance that points on the graph will lie from the origin. (If k =0, the equation graphs as a circle centered at the origin with a radius of b.) The rose will have n petals if n is odd and 2n petals if n is even. For examples of these graphs, click on the link below.

Click on the link below to examine several examples of graphs of the equation when a = 0, b = 2 and k is a noninteger.