Question

The equation of set points P such that PA² + PB² = 2K², where A and B are the points (3, 4, 5) and (–1, 3, –7), respectively is ______.

Options

• K² – 109

• 2K² – 109

• 3K² – 109

• 4K² – 109

Answer 1

The equation of set points P such that PA² + PB² = 2K², where A and B are the points (3, 4, 5) and (–1, 3, –7), respectively is 2K² – 109.

Explanation:

Let the coordinates of point P be (x, y, z).

Here, PA² = (x – 3)² + (y – 4)² + (z – 5)²

PB² = (x + 1)² + (y – 3)² + (z + 7)²

By the given condition: PA² + PB² = 2K²

We have

(x – 3)² + (y – 4)² + (z – 5)² + (x + 1)² + (y – 3)² + (z + 7)² = 2K²

i.e. 2x² + 2y² + 2z² – 4x – 14y + 4z = 2K² – 109