Find the equation of a circle passing through the point $(7,3)$ having radius $3$ units and whose centre lies on the line $y=x-1$.

Question

$\begin{array}{1 1}x^2+y^2-8x-6y+16=0\\x^2+y^2+8x-6y-16=0\\x^2+y^2+8x+6y+16=0\\x^2+y^2-8x-6y-16=0\end{array}$

Comments

why are they two equations and not one