A wall is inclined to the floor at an angle of 135^ . A ladder of length is resting on the wall. As the ladder slides down, its mid-point traces an arc of an ellipse. Then the area of the ellipse is

Step-by-step solution

Mid point ( h , k )= ( x - x ₁ 2 , x ₁ 2 ) Now ( x + x ₁ )²+ x ₁²= ² As 2 ~h +4 k = x + x ₁, 2 k = x , So required locus is array l 4( ~h +2 k )²+4 k ²= ² ~h ²+5 k ²+4 hk = ² 4 x ²+5 y ²+4 xy = ² 4 array Whose area is ² 4