maths variation

x ∝ y
Hence x = ky
where k is a constant.

(x² - 2xy + y²) / (x² + 2xy + y²)
= [(ky)² - 2(ky)y + y²] / [(ky)² +2(ky)(y) + y²]
= (k²y² - 2ky² + y²) / (k²y² + 2ky² + y²)
= (k² - 2k + 1)y² / (k² +2k + 1)y²
= (k² - 2k + 1) / (k² +2k + 1)
= constant

Hence, x² - 2xy + y² = constant * (x² + 2xy + y²)
i.e. x² - 2xy + y² ∝ x² + 2xy + y²