wolfram alpha doesn't plot implicit function with range

Recently I read an article in a magazine describing how an inverse graphing calculator on this page adds domains and ranges to implicit functions. Unfortunately the page is down and I can't see it for myself, so I tried to plot one of the formulas in wolfram alpha,

(y-x)^2 + (y^2 - 6*y + 8 + sqrt(y^4 - 12*y^3 + 52*y^2 - 96*y + 64))^2=0

but it doesn't plot it, it just shows an empty graph. It does however show the correct solution:

for 2 <= x <= 4, y=x

I also tried plotting it in geogebra and some online things that can handle implicit functions but they also just give empty graphs.

Is it too complicated? Is the formula correct? And if so why doesn't it plot the equation?

Thanks in advance.

Answer

Most numerical implicit function plotters actually depend on recognizing changes of sign. Basically, if you want to plot $f(x,y) = 0$, you start by sampling
a bunch of points $f(x_i,y_j)$, and you know that if this has opposite signs at two neighbouring points, there should be a piece of the curve somewhere between them. But if you have a function such that $f(x,y) \ge 0$ for all $x,y$, unless you are lucky enough to hit exactly on a point where $f(x,y) = 0$ you will only see positive values, and you will never detect the presence of
a curve. That's the case here, since your function is the sum of two squares.