IF THE  points A[3,4,5] AND B[-2,3,-7]  .FIND THE EQUATION OF THE SET OF THE POINTS P SUCH THAT [PA]=[PB]2 =K2

Dear Student,

Let Co-ordinates of P be (x , y) 

PA = x-32+y-42+z-52
PB = x--22+y-32+z--72 = x+22+y-32+z+72
PA2 = PB‚Äč2 
(x - 3)2 + (y - 4)+ (z - 5)= (x + 2)2 + (y - 3)+ (z + 7)2 
x2 - 6x + 9 + y2 - 8y + 16 + z2 - 10z + 25 = x2 + 4x + 4 + y2 - 6y + 9 + z2 + 14z + 49 
-10x - 2y - 24z + 9 + 16 +25 - 4 - 9 - 49 = 0
-10x - 2y - 24z - 12 = 0
5x + y + 12z + 6 = 0

Regards

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