Question

find the equation of the set of the points which are equal distance from the points a(1,-2,5) & b(0,4,-1)

Answer 1

Answer:

2x-12y+12z-13=0

Step-by-step explanation:

let P(x,y) be the point

which is equidistant from points A and B

so

PA=PB

square on both sides

PA²=PB²

now

distance = √[(x2-x1)² +(y2-y1)² +(z2-z1)²]

so using this

PA² = PB²

that gives

(x-1)²+(y+2)²+(z-5)² = (x-0)²+(y-4)²+(z+1)²

x²+1-2x+y²+4+4y+z²+25-10z = x²+y²+16-8y+z²+1+2z

on simplifying

-2x+12y-12z+13=0

2x-12y+12z-13=0