Given:

a(x^2)+2hxy+b(y^2)=1

a'(x^2)+2h'xy+b'(y^2)=1

for x,y in R

where a,b,h,a',b',h' are rational.

Prove that:

i)(h-h')^2-(a-a')(b-b')

ii)(ab'-a'b)^2+4(ah'-a'h)(bh'-b'h)

are both squares of rational numbers.

I proved i) easily by simply subtracting the two equations and getting a quadratic in (x/y). I have been trying to prove ii) but don't know where to begin. If some one could give me a nudge in the right direction it will be very helpful.

Thanks