Find the locus of appoint which moves such that the sum of the squares of its distance from the points `A(1,2,3),B(2,-3,5)a n dC(0,7,4)i s120.`

Explanation

To find the locus of a point \( P(x, y, z) \) such that the sum of the squares of its distances from the points \( A(1, 2, 3) \), \( B(2, -3, 5) \), and \( C(0, 7, 4) \) is 120, we will follow these steps:

### Step 1: Write the distance formulas
The distance from point \( P(x, y, z) \) to point \( A(1, 2, 3) \) is given by:
\[ PA = \sqrt{(x - 1)^2 + (y - 2)^2 + (z - 3)^2} \]
The distance from point \( P(x, y, z) \) to point \( B(2, -3, 5) \) is:
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