# A Stick Of Length 10 Units Rests Against The Floor And A Wall Of A Room. If The Stick Begins To Slide On The Floor Then The Locus Of Its Middle Point Is

Let the midpoint of Rod be h and k

The coordinates of A and B will be

$$\Rightarrow A \equiv (0,2k) and B \equiv (2h, 0)$$

Distance from A to B$$\rightarrow$$ AB = fixed (i.e length of rad is fixed)

$$\sqrt{(2k^{2}) + (2h^{2})} = 10$$ $$\Rightarrow 4(k^{2} + h^{2}) = 100$$ $$\Rightarrow k^{2} + h^{2} = 25$$

Now by expressing in a form of locus, we get:

$$x^{2} + y^{2} = 25$$

Therefore, the locus of its middle point is x^{2} + y^{2} = 25 \)

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