rectangular hyperbola question (1 Viewer)

[jjuunnee]

The point P(2p, 2/p) lies on the rectangular hyperbole xy=4
The equation of the normal to H at P is y - 2/p = p²(x - 2p)
The normal at P meets the hyperbola H again at the point Q. The midpoint of PQ is M.

i) Find the coordinates of M

ii) Find the cartesian equation of the locus of M as the position of P on H varies


Mainly need some help with the second part. thanks!

 

[integral95]

Hint: after you get M you then consider xy, then also consider x/y = -1\p^2 and y/x = -p^2