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JEE Main 2014 Mathematics question

MathematicsStraight LinesJEE Main 2014

A stair-case of length 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 staircase begins to slide on the floor, then the locus of P is:

Answer: (2)

Solution

Let the ends be (a, 0) on the floor and (0, b) on the wall with . P divides the staircase 1 : 2 starting from the wall end, so . Writing and :

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Question ID VK-104505