A stair - case of length l rests against a vertical wall and a floor of a room , let P be a point on the stair - case , nearer to its end on the wall , that divides its length in the ratio 1:2 . If the stair - case begins to slide on the floor , then the locus of P is :

Question

(a) an ellipse of eccentricity $\;\large\frac{1}{2}\;$(b) an ellipse of eccentricity $\;\large\frac{\sqrt{3}}{2}\;$ (c) a circle of radius $\;\large\frac{l}{2}\;$(d) a circle of radius $\;\large\frac{\sqrt{3}}{2} l\;$