Question

(a) Deduce the equation of the normal to the hyperbola xy = c² at the variable point P (cp, c/p).
(b) The normal at P meets the x-axis at Q. Find the Cartesian equation of the locus of the midpoint of PQ, expressing your answer in the form 8y^4 = f(x, y)

Answer 1

a) y=(p^2 x) +(c/p) -(c p^3)
b) f(x,y)=(c^4) - (2 c^2 xy)

Answer 2

I got (a), but how do you get (b)? Not sure how to do it

Answer 3

hope this helps...

Answer 4

ah, thanks! ^.^