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Question

A ladder of length ‘a’ rests against the floor and a wall of a room. If the ladder begins to slide on the floor, then the locus of its middle point is


A

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B

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C

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D

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Solution

The correct option is D


Let AB be the ladder. Let the cross section of the floor and wall be taken as the coordinates axes.

Let P(x, y) be the mid-point of AB whose locus is required. Then the coordinates of A and B are (2x, 0) and (0, 2y) respectively

Given, AB = a

(2x0)2+(02y)2=a4x2+4y2=a2or 4(x2+y2)=a2 Which is the required locus..


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