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I have a function $2x(x-1)=y(y-1)$. I tried to plot it in wolframalpha. However, plotting took a long time without showing any result.

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    $\begingroup$ try using geogebra $\endgroup$ – Nick Aug 11 '16 at 13:30
  • $\begingroup$ Do note it's not a function but a curve. $\endgroup$ – Vincenzo Oliva Aug 11 '16 at 14:47
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Use $2x(x-1)=y(y-1)$ as input and you get an implicit plot:

enter image description here

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If you complete the squares on both sides you get $$2x(x-1)=y(y-1)\\2(x^2-x)=y^2-y\\2(x-\frac 12)^2-\frac 14=(y-\frac 12)^2\\2(x-\frac 12)-(y-\frac 12)^2=\frac 14$$ which fits the standard form for a hyperbola, shifted $\frac 12$ unit right and up from the origin

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If you use polar coordinates $x=r \cos(t)$, $y=r \sin(t)$.

Solve the equation for $r$ to get $$r=\frac{4 \cos (t)-2 \sin (t)}{1+3 \cos (2 t)}$$ Make a polar plot $(0 \leq t\leq \pi)$ to get what Jan Eerland answered.

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