A circle has radius $3$ units and its centre lies on the line $y=x-1$. Then the equation of this circle if it passes through the point $(7, 3)$, is?

$(x - 7)^2 + (y - 6)^2 = 9 \\\Rightarrow x^2 + y^2 - 14x - 12y + 85 = 9, \\ \Rightarrow x^2 + y^2 - 14x - 12y + 76 = 0.$

$(x - 4)^2 + (y - 3)^2 = 9 \\ \Rightarrow x^2 - 8x + 16 + y^2 - 6y + 9 = 9, \\ \Rightarrow x^2 + y^2 - 8x - 6y + 25 = 9, \\ \Rightarrow x^2 + y^2 - 8x - 6y + 16 = 0.$