Question

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.

Answer 1

Let the coordinates of P be (x, y, z).
The coordinates of points A and B are (4, 0, 0) and (–4, 0, 0) respectively.
It is given that PA + PB = 10.

On squaring both sides again, we obtain
25 (x² + 8x + 16 + y² + z²) = 625 + 16x² + 200x
⇒ 25x² + 200x + 400 + 25y² + 25z² = 625 + 16x² + 200x
⇒ 9x² + 25y² + 25z² – 225 = 0
Thus, the required equation is 9x² + 25y² + 25z² – 225 = 0.