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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