Find the equation of the set of point P. the sum of whose distance A(4, 0,0) and B(-4, 0,0) is equal to 10.
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Step-by-step explanation:
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
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