Find the equation of set of points P such that PA 2 + PB 2 = 2 k 2 , where A and B are…

Mathematics · Class 11 · CBSEIntroduction to Three-dimensional Geometry

Find the equation of set of points P such that
PA2 + PB2 = 2k2, where A and B are the points (3, 4, 5) and (–1, 3, –7), respectively.
  1. x2 + y2 + z2 – 4x – 14y + 4z = 2k2 – 109
  2. 2x2 + 2y2 – 2z2 – 4x – 14y – 4z = 2k2 + 109
  3. 2x2 + 2y2 + 2z2 – 4x – 14y + 4z = 2k2 – 109
  4. None of these

Answer

(C) 2 x 2 + 2 y 2 + 2 z 2 – 4 x – 14 y + 4 z = 2 k 2 – 109

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