Question

find the set of points are equidistant from the point (3,4,5) (-2,1,4)​

Answer 1

Answer:

the points (1,2,3) and (3,2,−1)

MEDIUM

ANSWER

Let P(x,y,z) be the point that is equidistant from points A(1,2,3) and B(3,2,−1) .

i.e. PA=PB

⇒PA

2

=PB

2

⇒(x−1)

2

+(y−2)

2

+(z−3)

2

=(x−3)

2

+(y−2)

2

+(z+1)

2

⇒x

2

−2x+1+y

2

−4y+4+z

2

−6z+9=x

2

−6x+9+y

2

−4y+4+z

2

+2z+1

⇒−2x−6z+14=−6x+2z+14

⇒−2x−6z+6x−2z=0

⇒4x−8z=0

⇒x−2z=0

Thus the required equation is x−2z=0.