Question

A Stick Of Length $10Units$ 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

Answer 1

Let the midpoint of Rod be h and k

The coordinates of A and B will be

$A=(0,2k)AndB=(2h,0)$

Distance from A to B

AB = fixed (i.e length of rad is fixed)

$\sqrt{{\left(2k\right)}^2+{\left(2h\right)}^2}=10$

$$\begin{gathered} 4(k^2+h^2)=100 \\ {k}^2+h^2=25 \end{gathered}$$

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

$\mathbf{\therefore }\mathbf{}{\mathit{x}}^{\mathbf{2}}\mathbf{}\mathbf{+}\mathbf{}{\mathit{y}}^{\mathbf{2}}\mathbf{}\mathbf{=}\mathbf{}\mathbf{25}$

Therefore, the locus of its middle point is $x^2+y^2=25$