Sketch the curve $y^{2}=x^{2}+1$. By finding a parametric representation, or otherwise, determine the points on the curve where the radius of curvature is least, and compute its value there.

[Hint: you may use the fact that the radius of curvature of a parametrized curve $(x(t), y(t))$ is $\left(\dot{x}^{2}+\dot{y}^{2}\right)^{3 / 2} /|\dot{x} \ddot{y}-\ddot{x} \dot{y}|$.]