Question

The equation of the set of points which are equidistant from (1,2,3) and (3,2,-1).

• A. x = 2z
• B. x+2y+3z=0
• C. x+2z=0
• D. 2y-3z=0

Answer 1

The correct option is A

x = 2z

Let P(x,y,z) represent the set of points which equidistant from A(1,2,3) and B(3,2,-1).
Equating AP=BP using the distance formula, we have
$(x-1{)}^2+(y-2{)}^2+(z-3{)}^2=(x-3{)}^2+(y-2{)}^2+(z+1{)}^2\Rightarrow -2x-4y-6z=-6x-4y+2z\Rightarrow 4x-8z=0\Rightarrow x=2z$