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

Consider the two commonly opposite lines be x and y pivot and Let the point made by the line portion be θ on the x-hub. At that point the organize of end point on x-hub is P(Lcosθ,0)P(Lcosθ,0) and on y-pivot is Q(0,Lsinθ)Q(0,Lsinθ). 

Subsequently the point which isolates PQ in the proportion 1:2 can be computed as far as θ, 

i.e., S(x,y) will be with the end goal that, 

x=2L/3cosθx 

also, 

y=L/3sinθy 

In this way the locus will be given by: 

X2/4+y2=L2/9