8. If $x>0, y>0$, and $2 \lg (x-2 y)$ $=\lg x+\lg y$, then $\mathrm{x}: \mathrm{y}$ is:
(A) 43
(B) Is
(C) 1 or 43
(D) $\frac{1}{4}$.

Translate the above text into English, please retain the original text's line breaks and format, and output the translation result directly.
Answer: (A).
Solution 1 From the given equation, we have $(x-2 y)^{2}=x y$.
$$
x^{2}-5 x y+4 y^{2}=0 . \quad x=4 y \text { or } x=y .
$$

When $x=y$, $\lg (x-2 y)=\lg (-y)$ is impossible, so we discard $x=y$. $\therefore x=4 y$, i.e., $x: y=4$.

Solution 2 When $x$ : $y$ is 1 or $\frac{1}{4}$, $\lg (x-2 y)$ is undefined, hence (B).
(C),
(D) are not solutions.
Since the problem statement tells us that only one answer is correct, it must be (A).