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

Let the point of intersection of given two lines is P(h, k), which lies on both the lines. ∴ k+mh=a2m2+b2 and mk−h=a2+b2m2Squaring and adding, we get k+mh2+mk-h2=a2m2+b2a2+b2m21+m2k2+1+m2h2=a2m2+b2+a2+b2m2 1+m2k2+h2 =a2m2+1+b2m2+1∴  locus of h,kis x2+y2=a2+b2