Find the locus of the point, the sum of whose distances from the points `A(4,0,0)a n d\ B(-4,0,0)` is equal to 10.

Answer

N/a

Explanation

Let a point in set be `P-=(x,y,z)`.
Given that, PA+PB=10
`implies PA=10-PB`
`implies sqrt((x-4)^(2)+(y-0)^(2)+(z-0)^(2))`
`=10-sqrt((x+4)^(2)+(y-0)^(2)+(z-0)^(2))`
Squaring both sides,
`(x-4)^(2)+y^(2)+z^(2)=100+(z+4)^(2)+y^(2)+z^(2)-20sqrt((x+4)^(2)+y^(2)+z^(2))`
`implies sqrt(x^(2)+y^(2)+z^(2)+8x+16)=100+16x`
`implies 5sqrt(x^(2)+y^(2)+z^(2)+8x+16)=25+4x`
Again squaring both sides,
`25 (x^(2)+y^(2)+z^(2)+8x+16)=625+16x^(2)+200x`
`implies 9x^(2)+25y^(2)+25z^(2)-225=0`