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The locus of a point P which moves such ...

The locus of a point P which moves such that `PA^2 -PB^2 =2k^2` where A and B are (3, 4, 5) and (-1, 3, -7) respectively is

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Let P(a,b,c)
`PA^2-PB^2=2k^2`
`[(a-3)^2+(b-4)^2+(c-5)^2]-[(a+1)^2+(b-3)^2+(c+7)^2]=2k^2`
`[a^2-6a+9+b^2-8b+16+c^2-10c+25]-[a^2+1+2a+b^2+9-6b+c^2+49+14c]=2k^2`
`-6a-8b-10c+50-(2a-6b+14c+13)=2k^2`
`8a+2b+24c+9+2k^2=0`
`8x+2y+24z+9+2k^2=0`.
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