Given two polynomials f and g satisfying f(x) \geq g(x) for all real x, a separating line between f and g is a line h(x)=m x+k such that f(x) \geq h(x) \geq g(x) for all real x. Consider the set of all possible separating lines between f(x)=x^{2}-2 x+5 and g(x)=1-x^{2}. The set of slopes of these lines is a closed interval [a, b]. Determine a^{4}+b^{4}.