Find the equation of set of points P such that `P A^2+P B^2=2k^2`, where A and B are the points `(3, 4, 5)`and `(1, 3, 7)`, respectively.

Explanation

To find the equation of the set of points \( P \) such that \( PA^2 + PB^2 = 2k^2 \), where \( A(3, 4, 5) \) and \( B(1, 3, 7) \), we can follow these steps:

### Step 1: Define the coordinates of point P
Let the coordinates of point \( P \) be \( (h, k, l) \).

### Step 2: Calculate \( PA^2 \)
Using the distance formula, we can find \( PA^2 \):
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