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Find the equation of set of points P suc...

Find the equation of set of points P such that `P A^2+P B^2=2k^2`, where A and B are the points `(3, 4, 5)`and `(1, 3, 7)`, respectively.

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Given,
coordinates of A and B are `(3,4,5) and (−1,3,−7) `respectively.
Let the coordinates of point P be (x,y,z).
Given, `PA^2+PB^2=K^2`
`⇒(x−3)^2+(y−4)^2+(z−5)^2+(x+1)^2+(y−3)^2+(z+7)^2=K^2`
`=>x^2−6x+9+y^2−8y+16+z^2−10z+25+x^2+2x+1+y^2−6y+9+z^2+14z+49=K^2`
`⇒2x^2+2y^2+2z^2−4x−14y+4z+109=K^2`
...
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