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Any ideas about why Desmos/Wolfram Alpha) does not show $(0,0)$ as a part of the curve $$2^2 x^2 + 4^2 y^2 = (x^2 + y^2)^2$$ will be appreciated.

Am I missing something or is it a bug?

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Changing coordinates

$$ x = r\cos\theta\\ y=r\sin\theta $$

we get

$$ r^2 (r^2 + 6 \cos(2\theta)-10) =0 $$

so clearly appear the two solutions

$$ r = 0\\ r^2 + 6 \cos(2\theta)-10=0 $$

enter image description here

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    $\begingroup$ This answer should be upvoted $\endgroup$ – Cloud JR Dec 15 '18 at 12:47
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Not, it's not a bug. Yes, $(0,0)$ belongs to that curve, but it is an isolated point of the curve. In other words, no nearby point belongs to the curve. That's why you can't see it.

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