<s>[INST] Producing circles with $r^2=x^2+y^2$ $r^2=x^2+y^2\ +\pi $ produces graph with two circles :
$r = 2$

This graph was produced using Desmos, is this correct or a quirk of the graph software ?
Ive noticed $\forall n \epsilon N [r^2=x^2+y^2+n\pi]$ appears to produce same circle, so $r^2=x^2+y^2\ +3\pi $ produces same circle as $r^2=x^2+y^2\ +4\pi $  :

Why is this the case, should each circle not be differing sizes ?
 [/INST] The equation $2^2=x^2+y^2+\pi$ is equivalent to $x^2+y^2=4-\pi=0.8584\ldots$, which produces a circle of radius $\sqrt{4-\pi}=\sqrt{0.8584\ldots} = 0.9265\ldots$, which is the red circle in the top figure.
The equation $2^2=x^2+y^2+3\pi$ is equivalent to $x^2+y^2=4-3\pi=-5.4247\ldots$. Since that's a negative number, there are no solutions to the equation for real numbers $x$ and $y$. So there is no red circle in the bottom figure.
I don't know what the orange circle means in each figure. Try consulting the software's manual?
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