Find the equation of set of points P, the sum of whose distance from A(4,0,0) and B(-4,0,0) is equal to 10

Explanation

Let the point be P(x,y,z).
Given that PA+PB=10
`implies sqrt((x-2)^(2)+y^(2)+z^(2))+sqrt((x+2)^(2)+y^(2)+z^(2))=10`
`implies sqrt((x+2)^(2)y^(2)+z^(2))=10-sqrt((x-2)^(2)+y^(2)+z^(2))`
Squaring both sides, we get
`x^(2)+4x+4+y^(2)+z^(2)`
`=100+x^(2)-4z+4+y^(2)+z^(2)-20sqrt(x^(2)+y^(2)+z^(2)-4x+4)`
`implies 8x-100= - 20sqrt(x^(2)+y^(2)+z^(2)-4x+4)`
`implies 2x-25= - 5sqrt(x^(2)+y^(2)+z^(2)-4x+4)`
Again squaring both sides
`4x^(2)-100x+625=25(x^(2)+y^(2)+z^(2)-4x+4)`
`=21x^(2)_25y^(2)+25z^(2)=525`.