The locus of point of intersection of the lines y+mx=a2m2+b2 and my−x=a2+b2m2 is

Let the point of intersection of given two lines be Ph,k, which lies on both the lines ∴   k+mh=a2m2+b2and mk−h=a2+b2m2Squaring and adding, we get 1+m2k2+1+m2h2=a2m2+b2+a2+b2m2Therefore, locus is x2+y2=a2+b2m21+m2k2+1+m2h2=a2m2+b2+a2m2Therefore, locus is x2+y2=a2+b2.