Example 2. Let $A(a, 0), B(0, b)$ be known points, find the moving point $P(x, y)$ that satisfies $S_{\triangle O A P}=2 \widetilde{B}_{\triangle O P B}$.
Solution: As shown in Figure 2, draw $P P^{\prime} \perp o x$ axis at $P^{\prime}$, and $P P^{\prime \prime} \perp o y$ axis at $P^{\prime \prime}$. Take $S_{\triangle O P A}=l$ as the parameter, then
$$
\begin{array}{l}
|y|=\left|P P^{\prime}\right|=\frac{2 S_{\triangle O A P}}{|O A|}=\frac{2 t}{|a|}, \\
|x|=\left|P P^{\prime \prime}\right|=\frac{2 S_{\triangle O B P}}{|O B|}=\frac{t}{|b|}
\end{array}
$$

Eliminating the parameter and removing the absolute value signs, we get $y= \pm \frac{2 b}{a} x$.