What does the graph of a polar equation look like when $r=b+a\cos\theta$ and $b>a$ and why? The graph of the polar equation $r=a+a\cos(\theta)$ is a cardioid. The graph of $r=a+b\cos(\theta)$ when $a<b$ is a limaçon.
What does the graph of $r=b+a\cos(\theta); b>a$ look like? What is the reason for these shapes?  
When I plug it into a calculator, it looks like an off-center circle. Is this right? What is making it look the way it does?

No, it cannot be a circle, because if you vary a parameter continuously from $a=b$, you get a curve that departs from the Cardioid progressively.
With $b<a$, the cusp of the Cardioid becomes the double point of the Limaçon. With $b>a$, that cusp disappears smoothly. The curve remains asymmetric.


We can find the implicit equation of these curves from
$$\rho^2=b\rho+ax$$ or
$$(x^2+y^2-ax)^2=b^2(x^2+y^2).$$
This is not the equation of a circle.
