1.

Find the equation of the set of points P which moves so that its distances from the points `A(3,4,-5) and B(-2,1,4)` are equal.

Answer» Let `P(x,y,z)` be any point on the give curve, and let `A(3,4,-5) and B(-2,1,4)` be the given points.
Then, PA=PB
`rArr PA^(2)=PB^(2)`
`rArr (x-3)^(2)+(y-4)^(2)+(z+5)^(2)=(x+2)^(2)+(y-1)^(2)+(z-4)^(2)`
`rArr 10x+6y-18x-29=0`
Hence, the required curve is `10x+18z-29=0`


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