Let AB be a line segment of length 4 units with the point A on the line y = 2x and B on the line y = x. Then the locus of middle point of all such line segment is

Let B=(α,α) and middle point AB is (h,k), Then A≡(2h−α,2k−α) lies on y = 2x thenα=4h−2k........(1)|AB|=4⇒[h−(4h−2k)]2+[k−(4h−2k)]2=4 or 25h2+13k2−36hk=4Required locus is 25x2+13y2−36xy−4=0Here, h2