A man running a racecourse notes that the sum of the distances from the two flag posts from him is always 10 m and the distance between the flag posts is 8 m. Find the equation of the posts traced by the man.

Explanation

To find the equation of the posts traced by the man, we can follow these steps:

### Step 1: Understand the Problem
We have two flag posts, and the sum of the distances from a point (the man) to these two flag posts is constant (10 m). The distance between the two flag posts is 8 m.

### Step 2: Identify the Foci
Let’s denote the two flag posts as points \( F_1 \) and \( F_2 \). Since the distance between the flag posts is 8 m, we can place them on the x-axis for simplicity. Therefore, we can set:
- \( F_1 = (-4, 0) \)
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