It 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 (PA)2 + (PB)2 = K2, where K is a constant.

# It 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 (PA)2 + (PB)2 = K2, where K is a constant.

1. A

$2\left({\mathrm{x}}^{2}+{\mathrm{y}}^{2}+{\mathrm{z}}^{2}\right)+4\mathrm{x}+14\mathrm{y}+4\mathrm{z}+109-{\mathrm{K}}^{2}=0$

2. B

$2\left({\mathrm{x}}^{2}+{\mathrm{y}}^{2}+{\mathrm{z}}^{2}\right)-4\mathrm{x}-14\mathrm{y}+4\mathrm{z}+109-{\mathrm{K}}^{2}=0$

3. C

${\mathrm{x}}^{2}+{\mathrm{y}}^{2}+{\mathrm{z}}^{2}+4\mathrm{x}+14\mathrm{y}+4\mathrm{z}+109-{\mathrm{K}}^{2}=0$

4. D

None of the above

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### Solution:

Let the point P is (x, y, z).

Given  (PA)2 + (PB)2 = K2

$\begin{array}{r}⇒2{\mathrm{x}}^{2}+2{\mathrm{y}}^{2}+2{\mathrm{z}}^{2}-4\mathrm{x}-14\mathrm{y}+4\mathrm{z}+109-{\mathrm{K}}^{2}=0\\ ⇒2\left({\mathrm{x}}^{2}+{\mathrm{y}}^{2}+{\mathrm{z}}^{2}\right)-4\mathrm{x}-14\mathrm{y}+4\mathrm{z}+109-{\mathrm{K}}^{2}=0\end{array}$

which is the required equation.  Register to Get Free Mock Test and Study Material

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