If $x_1,x_2$ are the roots of the equation $x^2+bx+c=0$ and $y_1$ and $y_2$ are the roots of $y^2+qy+r=0$ then the equation of the circle having $\left(x_1,y_1\right)$ and $\left(x_2,y_2\right)$ as ends of diameter is