變分題目、數學高手請進

2a)
let (y^2 - x^2) = k/((1/x^2) - (1/y^2)),k is constant
y^2 - x^2 = k/((y^2 - x^2) / x^2y^2)
y^2 - x^2 = k(x^2y^2)/(y^2 - x^2)
(y^2 - x^2)^2 = k(x^2y^2)<--------(y^2 - x^2)^2 is directly varies to (x^2y^2)
y^2 - x^2 = q(xy)<---------------(y^2 - x^2 ) is directly varies to xy

2b)
let (y^2 + x^2) = R/{[(1/x^2) - (1/y^2)]},where R is constant
(y^2 + x^2) = R(x^2y^2)/(y^2 - x^2) <---------by part a
y^4 - x^4 = R(x^2y^2)
So,
(y^4 - x^4) is directly varies to x^2y^2

(a) Let (y^2 - x^2) (1/x^2 - 1/y^2)= k
(y^2 - x^2) (y^2 - x^2) / (x^2y^2)= k
(y^2 - x^2)^2 = kx^2y^2
(y^2 - x^2) = (開方k)xy
(y^2 – x^2) 正變於xy (題目打錯)

(b) 同上，差唔多