find the equation of set of points P such that PA^{2} +PB^{2}=2K2 ,where A&B are the points (3,4,5) and (-1,3-7) respectively

** hey.. i think it's frm NCERT...!! isn't it..??**

**here's d answr..!**

**Let the coordinates of point P be (x, y, z).**

**Here PA sq = (x – 3) ^{2 }+ (y – 4)^{2}+ ( z – 5)^{2}**

**PB ^{2 } = (x + 1)^{2} + (y – 3)^{2} + (z + 7)^{2}**

**By the given condition PA ^{2}+ PB^{2} = 2k^{2}, we have**

**(x – 3) ^{2} + (y – 4)^{2}+ (z – 5)^{2} + (x + 1)^{2}+ (y – 3)^{2 }+ (z + 7)^{2} = 2k^{2}**

**i.e., 2x ^{2}+ 2y^{2} + 2z^{2} – 4x – 14y + 4z = 2k^{2} – 109.**

**hope i helped.. :) :)**

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