A stick of length l  moves on coordinate axes. The Locus of midpoint of the stick is

Let xa+yb=1  meets x−axis at A(a,0) y−axis  at B(o,b)AB=l,  ⇒a2+b2=l2 ___________(1)Locus point (x,y)=midpoint of AB(x,y)=(a2,b2)⇒a=2x,  b=2ySubstitute  in (1)  ⇒4x2+4y2=l2