An iron rod of length 2l is sliding on two mutually perpendicular lines,. Then the locus of the midpoint of the rod is

Let rod meets the coordinate axes at the points (a,0) and (0,b)

Given that a²+b²=4l²

^{let (x,y) be locus of mid point of rod}

$\Rightarrow$x=a/2, y=b/2
Locus is  ${\mathrm{x}}^2+{\mathrm{y}}^2=\frac{{\mathrm{a}}^2+{\mathrm{b}}^2}{4}={\mathrm{l}}^2$
$\therefore$Locus is a circle