genus of the field $\mathbb{R}(x,y)$ where $x^2+y^2+1=0$

Question

I have come across a problem while reading Chevelley's "Introduction to the theory of algebraic functions of one variable", in which he says that the genus of the field $L=\mathbb{R}(x,y)$ is 0, where $x$ is transcendental over $\mathbb{R}$ and $y$ satisfies $x^2+y^2+1=0$ and he further states that every place of this field is of degree 2. Here $L$ is an algebraic function field (i.e a finite field extension of a purely transcendental extension of $\mathbb{R}$). Can anyone explain how is it possible?