1.

Find the locus of appoint which moves such that the sum of the squares ofits distance from the points `A(1,2,3),B(2,-3,5)a n dC(0,7,4)i s120.`

Answer» Let `P(x,y, z)` be any point on the locus. Then `PA^(2)+PB^(2)+PC^(2)=120`
`rArr " "(x-1)^(2)+(y-2)^(2)+(z-3)^(2)+(x-2)^(2)+(y+3)^(2)+(z-5)^(2) +(x-0)^(2)+(y-7)^(2)`
`" "+(z-4)^(2)= 120`
`" "3x^(2)+3y^(2)+3z^(2)-6x-12y-24z+117=120`
`" "x^(2)+y^(2)+z^(2)-2x-4y-8z-1=0`
This represents a sphere with centre at (1, 2, 4) and radius equal to `sqrt(1^(2)+2^(2)+4^(2)+1) =sqrt(22)`.


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