Consider a triangle $\triangle$ whose two sides lie on the $x$-axis and the line $x + y + 1 = 0$. If the orthocenter of $\triangle$ is $(1, 1)$, then the equation of the circle passing through the vertices of the triangle $\triangle$ is;
a. $x^2 + y^2 - 3x + y = 0$
b. $x^2 + y^2 + x + 3y = 0$
c. $x^2 + y^2 + 2y - 1 = 0$
d. $x^2 + y^2 + x + y = 0$