prove that the equation of the normal to the rectangular
hyperbola xy = c^2 at the point P(ct, c/t) is t^3 x −ty = 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 QR, as P varies is 2c^2 xy + y^4 = c^4 .