First slide

Equation of line in Straight lines

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

Moderate

A

x²+ y² = a²
B

2(x² + y²) = a²
C

x² + y²= 2a²
D

4(x² + y²) = a²

Solution

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
$\Rightarrow \sqrt{{(2 x - 0)}^{2} + {(0 - 2 y)}^{2}} = a \Rightarrow 4 x^{2} + 4 y^{2} = a^{2}$
or 4(x² + y²) = a², which is the required locus

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