Does the curve $2^2 x^2 + 4^2 y^2 = (x^2 + y^2)^2$ pass through $(0,0)$?

Question

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?

Answer 1

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

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

Answer 2

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.