A ladder of length ‘a’ rests against the floor and a wall of a room. If the ladder begins to slide on the floor, then the locus of its middle point is

Let AB be the ladder. Let the cross section of the floor and wall be taken as the coordinates axes. Let P(x, y) be the mid-point of AB whose locus is required. Then the coordinates of A and B are (2x, 0) and (0, 2y) respectively.Given, AB = a⇒2x-02+0-2y2=a⇒4x2+4y2=a2or 4(x2 + y2) = a2, which is the required locus