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Question Number 93483 by Rio Michael last updated on 13/May/20

prove that the equation of the normal to the rectangular

hyperbola x y = c^{2} at the point P (c t, c / t) is t^{3} x - t y = c (t^{4} - 1) .

the normal to P on the hyperbola meets the x - axis at Q and the

tangent to P meets the yaxis at R . show that

the locus of the midpoint oc Q R, as P varies is 2 c^{2} x y + y^{4} = c^{4} .