# How to sketch $(y^2-2)^2+(x^2-2)^2=2$? [closed]

I get the overall idea, but why is the shape of these figures not a circle?

• desmos.com/calculator/0y5iawztgg Nov 5, 2017 at 19:41
• $(x-2)^2+(y-2)^2=2$ is a circle. A quartic equation normally does not have a circular graph. Nov 5, 2017 at 19:41
• this Looks nice wolframalpha.com/input/… Nov 5, 2017 at 19:43
• @DonaldSplutterwit, thanks for your link. I got a pillow shape using $(x^2-2)^2+(y^3-2)^2=7$. Nov 5, 2017 at 19:45

Consider new frame with coordinate axes defined as $X=x^2$ and $Y=y^2$.
In this new frame of reference, the equation you mentioned will be a perfect circle with center at (2,2) and radius of $\sqrt 2$.
But every point on this new frame of reference will have, 4 copies in the original $x,y$ frame. Why?
A point $(X_0,Y_0)$ in new frame will have $4$ copies which will be $(\sqrt {X_0},\sqrt {Y_0}),(\sqrt {X_0},-\sqrt {Y_0}),(-\sqrt {X_0},\sqrt {Y_0}),(-\sqrt {X_0},-\sqrt {Y_0})$.
Since the circle in new reference frame lies completely in 1st quadrant, therefore the circle will be replicated into $4$ figures in $4$ different quadrants in original frame of reference.