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If A and B be the points (3, 4, 5)and (-...

If A and B be the points `(3, 4, 5)`and `(-1, 3, -7)`, respectively, find the equation of the set of points P such that `P A^2+P B^2=k^2`, where k is a constant.

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To find the equation of the set of points \( P \) such that \( PA^2 + PB^2 = k^2 \), where \( A(3, 4, 5) \) and \( B(-1, 3, -7) \), we will follow these steps: ### Step 1: Define the coordinates of point \( P \) Let the coordinates of point \( P \) be \( (x, y, z) \). ### Step 2: Calculate \( PA^2 \) Using the distance formula, the distance \( PA \) from point \( P \) to point \( A \) is given by: \[ ...
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