Given that, $(x+y) = \text{K} (x-y)$
$\Rightarrow x + y = \text{K}x - \text{K}y$
$\Rightarrow y + \text{K}y = \text{K}x -x$
$\Rightarrow x(\text{K} -1) = y(\text{K} + 1)$
$\Rightarrow \dfrac{x}{y} = \dfrac{(\text{K} + 1)}{(\text{K} -1)}$
$\Rightarrow \dfrac{x}{y} = \text{Constant}$
Correct Answer: D