$y=f\left(x\right)$ is a parabola of the form $f\left(x\right)=x^2+bx+1,b$ is a parameter. The tangent line to $y=f\left(x\right)$ is drawn at the point where $y=f\left(x\right)$ cuts Y – axis, is also touches $x^2+y^2=r^2(r>0).$ Then the value of  $\underset{b\to 0}{\lim }\frac{\sqrt{r_{\max }-r}}{\sin b}$ is