Identify the graph - 2

As $x \to \pm \infty$ , $y \to \frac12$ ; as $y \to \pm \infty$ , $x \to \frac12$ .

These asymptotes intersect at the hyperbola's centre, $\boxed{\left(\frac12,\frac12\right)}$ .

Solving for $y$ in terms of $x$ yields $y = \frac{1}{2} + \frac{0.5}{2x-1}$ , which has a vertical asymptote at $x = \frac{1}{2}$ and a horizontal asymptote at $y = \frac{1}{2}.$ Thus the hyperbola's center is the intersection of these two asymptotes: $\boxed{(\frac{1}{2}, \frac{1}{2})}.$