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.
• B.
• C.
• D.

Answer 1

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

$\Rightarrow \sqrt{(2x-0{)}^2+(0-2y{)}^2}=a\Rightarrow 4x^2+4y^2=a^{2}or4(x^2+y^2)=a^2$ Which is the required locus..