<s>[INST] curve of $(x^2+y^2)^2=2(x^2-y^2)$ The diagram shows the curve $(x^2+y^2)^2=2(x^2-y^2)$ and one of its maximum points $M$. Find the coordinates of $M$. 
My attempt.
Differentiate the equation and I got 
$\frac{dy}{dx}=-\frac{x(x^2+y^2-1)}{y(x^2+y^2+1)}$
How should I proceed?
 [/INST] I think you take the top part set it to zero $x(x^2+y^2-1)=0$, since thats how you get the critical numbers. Then you have :
$x=0$ or $y=\sqrt{1-x^2}$
plug y back into original formula and solve to get something like 
 $x=\pm \sqrt{\frac{3}{4}}$ so max would be at one of those $x$ values.
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