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# Find the locus of P if PA2 + PB2 = 2k2 where A and B are the points (3,4,5) and (-1,3,-7).

Asked by Topperlearning User 20th February 2015, 10:30 AM

Let P(x,y,z) be the point whose locus is to be found, Now

PA2 + PB2 = 2k2.

(x - 3)2 + (y - 4)2 + (z - 5)2 + (x + 1)2 + (y - 3)2 + (z + 7)2 =2k2

x2 - 6x + 9 + y2 - 8y + 16 + z2 - 10z + 25 + x2 + 2x + 1 + y2 - 6y + 9 + z2 + 14z + 49 = 2k2

2x2 + 2y2 + 2z2 - 4x - 14y + 4z + 109 = 2k2.

Answered by Expert 20th February 2015, 12:30 PM
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