lx+my+n =0 is normal to xy =1 then possible values of l and m

consider general Eqn of rectangular hyperbola xy=c2

Diff the eqn then xdy/dx+y=0 slope of normal is -dx/dy which is equal to x/y slope of normal at general point(ct,c/t) slope of normal is ct/c/t=t2 therefore eqn of normal at point (ct,c/t) is y-c/t=t2(x-ct) which is equal to t3x-yt-ct4=0 by comparison with given line l=t3 m=-t therefore l+m3=0