一、(20 points) On the square, 5 loudspeakers are to be installed, divided into two groups. The first group has 2 loudspeakers installed together, and the second group has 3 loudspeakers installed together. The distance between the two groups is 50 meters. Where should one stand to hear the sound from both groups equally strong?
Let $x$ represent the distance from the point to the smaller group, then the distance from this point to the larger group is $(50-x)$. Since sound intensity is inversely proportional to the square of the distance, we get the equation:
$$
\frac{2}{3}=\frac{x^{2}}{(50-x)^{2}}.
$$

Simplifying, we get $x^{2} + 200x - 5000 = 0$.
Solving, we get $x_{1}=22.5$, $x_{2}=-222.5$.
Thus, the point where the sound intensity is equal is 22.5 meters from the smaller group of speakers and 50-22.5 = 27.5 meters from the larger group (*).

The other point is in the opposite direction, 222.5 meters from the smaller group of speakers, and 222.5 + 50 = 272.5 meters from the larger group (*).

These two points on the line are where the sound intensity is equal. Therefore, the points that meet the condition form a circle with these two points as the endpoints of its diameter.