variation 10marks

Since (x² + y²) varies as (x² - y²),
then (x² + y²) = k(x² - y²) where k is constant.
x² + y² = kx² - ky²
kx² - x² = ky² + y²
(k - 1)x² = (k + 1)y²
x²/y² = (k + 1)/(k - 1)
x/y = ±√[(k + 1)/(k - 1)]

Put h = ±√[(k + 1)/(k - 1)]
Then, x/y = h
x = hy

(x + y) / (x - y)
= (hy + y) / (hy - y)
= (h + 1)y / (h - 1)y
= (h + 1) / (h - 1)
= constant

Since (x + y) / (x - y) = constant,
then (x + y) = constant * (x - y)
Hence, (x + y) varies as (x - y)