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.

Do note it's not a function but a curve. – Vincenzo Oliva Aug 11 '16 at 14:47 — Vincenzo Oliva, Aug 11 '16 at 14:47

score 2 · Answer 1 · answered Aug 11 '16 at 13:41

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

score 1 · Answer 2 · answered Aug 11 '16 at 13:40

1

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.

answered Aug 11 '16 at 13:40

Claude Leibovici

260,315

score 0 · Accepted Answer · answered Aug 11 '16 at 13:33

0

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

answered Aug 11 '16 at 13:33

Jan Eerland

28,671

How would this function look like?

3 Answers3