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

    2x2+y2+z2+4x+14y+4z+109K2=0

  2. B

    2x2+y2+z24x14y+4z+109K2=0

  3. C

    x2+y2+z2+4x+14y+4z+109K2=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

     (x3)2+(y4)2+(z5)2+(x+1)2+(y3)2+(z+7)2=K2

     x2+96x+y2+168y+z2+2510z+x2+1+2x+y2+96y+z2+49+14z=K2 

    2x2+2y2+2z24x14y+4z+109K2=02x2+y2+z24x14y+4z+109K2=0

    which is the required equation. 

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