Normal of a rectangular hyperbola (1 Viewer)

[Newto]

This is a questions off the 2002 Barker Trial Paper, I haven't been able to get it and I couldn't find solutions anywhere, can anyone solve it.

5. The normal at P(ct, c/t ) to the hyperbola xy = c² meets the curve again at Q.
(a) Prove that the equation of the normal is xt³ − ty = ct⁴ − c
(b) Find the coordinates of Q.
(c) A line from P through the origin meets the hyperbola again at R. Prove that PR is perpendicular to QR.

 

[DatAtarLyfe]

 

[Newto]

Thanks heaps