rectangular hyperbola question (1 Viewer)

jjuunnee

Active Member
Joined
Mar 16, 2016
Messages
169
Location
Sydney
Gender
Female
HSC
2018
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

Well-Known Member
Joined
Dec 16, 2012
Messages
779
Gender
Male
HSC
2013
Hint: after you get M you then consider xy, then also consider x/y = -1\p^2 and y/x = -p^2
 

Users Who Are Viewing This Thread (Users: 0, Guests: 1)

Top