Find the equation of the set of points P, the sum of whose distances from A (4, 0, 0) and B (–4, 0, 0) is equal to 10

Explanation

To find the equation of the set of points \( P \) such that the sum of the distances from points \( A(4, 0, 0) \) and \( B(-4, 0, 0) \) is equal to 10, we can follow these steps:

### Step 1: Define the point \( P \)
Let the coordinates of point \( P \) be \( (x, y, z) \).

### Step 2: Write the distance formulas
Using the distance formula, the distance \( PA \) from point \( P \) to point \( A \) is given by:
\[
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