Question

The locus of a point which is equidistant from the points P(0,2,3) and Q(2,-2,1) will be .

• A. x - 2y - z + 1 = 0
• B. x - 2y + z + 1 = 0
• C. x + 2y - z + 1 = 0
• D. x - 2y - z - 1 = 0

Answer 1

The correct option is A x - 2y - z + 1 = 0

Let A(x,y,z) be a point which is equidistant from the given Points.
i.e. AP=AQ
$\mathrm{Also},{\mathrm{AP}}^2={\mathrm{AQ}}^2\Rightarrow {(x-0)}^2+{(y-2)}^2+{(z-3)}^2={(x-2)}^2+{(y+2)}^2+{(z-1)}^2\Rightarrow 4-4y+9-6z=4-4x+4+4y+1-2z\Rightarrow 4x-8y-4z+4=0\Rightarrow x-2y-z+1=0$