We assume that a(t) is an arclength-parametrized C curve that contained in a plane, (we also know that a(t) in C means that a has continuous derivatives up to third order.) Here we supposet exist inside the bound [a, b]. Now we can add a new"parallel" curve which has B(t) = a(t) + N(t), e is some constant and greater than 0 a) please prove that is a regular curve whenever is small enough, (for example whenever 0 < e < o for some 0 > 0. b) Now please represent the curvature of in terms of the curvature of a