If the circle x2 + y2 + 4x + 2y - 4 = 0 is reflected in a mirror to become the circle x2 + y2 + 6x + 4y + 4 = 0, the mirror is lying along the straight line

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We havex2+y2+4x+2y-4=0Centre is -2,-1x2+y2+6x+4y+4=0Centre is -3,-2Mid point of two centres must lie on mirror.-2-32,-1-22=-52,-32Hence equation of mirror is y+32=mx+522y+3=m2x+52mx-2y+5m-3=0Now distance of line from centres of both the circle must be same.2m-2-2-1+5m-34m2+4=2m-3-2-2+5m-34m2+4-4m+2+5m-3=-6m+4+5m-32m=2m=1Hence mirror is2x-2y+2=0x-y+1=0

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