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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 :

(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 $\;\large\frac{\sqrt{3}}{2} l\;$

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