How would this function look like?

Question

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.

Answer 1

Use $2x(x-1)=y(y-1)$ as input and you get an implicit plot:

Answer 2

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.

Answer 3

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