Maximal ideal in $\mathbb{R}[x,y]/ (x^2 + y^2 -1)$

Question

I need to show that the ideal $(\overline{x},\overline{y} -1 )$ is maximal in $\mathbb{R}[x,y]/ (x^2 + y^2 -1)$.

Thanks in advance for any help.

Answer 1

Hint. Set $R=\mathbb{R}[x,y]/ (x^2 + y^2 -1)$. Then $R/(\overline{x},\overline{y} -1 )\simeq\mathbb{R}[x,y]/(x,y-1)$.