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

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?

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

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

• This answer should be upvoted – Cloud JR Dec 15 '18 at 12:47

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.