Question of how to write certain response 

What is the domain of the function $$f(x,y)=\frac{1}{x^2+y^2-1}$$


The answer is clear, right?!
$$x^2+y^2-1\neq 0\Longrightarrow x^2+y^2\neq1$$What is the point contained in the circle of radius one, but my question is, how to write the domain of this function.
Can you help me?
$$D(f)=\{x,y\in \mathbb{R}\mid x^2+y^2\neq 1 \}?$$

The domain is a set of ordered pairs, so I would write it as $D(f)=\{(x,y)\in \mathbb{R^2}\mid x^2+y^2\neq 1 \}$
