Minimum distance between the curves y^2=x-1 and x^2=y-1 is equals to

Start finding y in terms of x for both equations y^2= x-1 is the inverse function to x^2 = y - 1 the two functions are symmetrical across the line y = x the point that minimized the distance then from one function to y =x will have a corresponding point on the other function, and the distances between these two points will be the minimal distance the point of minimal distance will be where dy/dx = 1 y = x^2 + 1 dy/dx = 2x = 1 x = 1/2 y = (5/4) d ((1/2, 5/4) , (5/4, 1/2)) (2(5/4-1/2)^2)^1/2 (3/4) sqrt 2