Plot of $n$ concentric circles at once?

Question

While we plot the Equation of $$(x^2+y^2-1)=0$$ we get:

While we plot $$(x^2+y^2-4)=0$$ we get:

So What will happen if we plot

$$\prod\limits_{i=1}^{i=n} \Big({(x-a)^2+(y-b)^2-i^2}\Big)=0$$

??

Will we get Concentric Circles?

Also...WolframAlpha agrees! (Link of concentric circles with radii=1,2,3)

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Also if not...What will be the Cartesian/polar equation of concentric circles?

Answer 1

Hint:

If $\hspace{0.25cm}\displaystyle\prod_{k=1}^n a_k = 0\hspace{0.25cm}$ then for some $K$, $a_K = 0$.

Now let $a_k = (x^2+y^2 - k^2)$... what can you conclude?