1.

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

Answer» Let `P(x,y,z)` be an arbitrary on the given curve. Then,
`PA+PB=10`
`rArr sqrt((x-4)^(2)+y^(2)+z^(2))+sqrt((x+4)^(2)+y^(2)+z^(2))=10`
`rArr sqrt((x-4)^(2)+y^(2)+z^(2))=10-sqrt((x+4)^(2)+y^(2)+z^(2))`
`rArr (x+4)^(2)+y^(2)+z^(2)=100+(x-4)^(2)+y^(2)+z^(2)-20sqrt((x-4)^(2)+y^(2)+z^(2))" " [ " on squaring both side of (i)"]`
`rArr 16x=10-20 sqrt((x-4)^(2)+y^(2)+z^(2))`
`rArr 5sqrt((x-4)^(2)+y^(2)+z^(2))=(25-4x)`
`rArr 9x^(2)+25y^(2)+25z^(2)-225=0`
Hence, the required equation of the curve is
`rArr 9x^(2)+25y^(2)+25z^(2)-225=0`


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