# 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 : Option 1) an ellipse of eccentricity Option 2) an ellipse of eccentricity Option 3) a circle of radius Option 4) a circle of radius

As we learnt in

Selection formula -

- wherein

If P(x,y) divides the line joining A(x1,y1) and B(x2,y2) in ration

and

Eccentricity -

- wherein

For the ellipse

We know length = l

so, x2, + y2 = l2

now using section formula

P(h, k) is

x = 3h;

, an ellipse

so

Option 1)

an ellipse of eccentricity

this is incorrect

Option 2)

an ellipse of eccentricity

this is correct

Option 3)

this is incorrect

Option 4)

this is incorrect

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