Find the equation of the set of the points `P` such that is distances from the points `A(3,4,-5)a n d\ B(-1,2,4)` are equal.

Explanation

Given points `A(3,4,-5)a n d\ B(-1,2,4)`
There exist some extent `P(x,y,z)` such as distances from the points `A(3,4,-5)a n d\ B(-1,2,4)`
are equal.
so, form given data of question `PA=PB`
`PA^2=PB^2`
`=>(x-3)^2+(y-4)^2+(z+5)^2=(x+1)^2+(y-2)^2+(z-4)^2`
`=>x^2+9-6x+y^2+16-8y+z^2+25+10z=x^2+1+2x+y^2+4-4y+z^2+16-8z`
`=>10x+6y-18z-29=0`
`10x+6y-18z-29=0`is the equation of set point `P`