Question

A point moves such that sum of square of its distances from $x-$ axis and $y-$axis is equal to square of its distance from $yz-$plane, then the locus of that point is

• A. $x-$axis
• B. $y-$axis
• C. $z-$axis
• D. $xz-$plane

Answer 1

The correct option is A $x-$axis

Let point is $P(x,y,z)$ , then
Distance from $x-$axis $=\sqrt{y^2+z^2}$,
Distance from $y-$axis $=\sqrt{x^2+z^2}$,
Distance from $yz-$plane $=|x|$
According to statement,
$(y^2+z^2)+(x^2+z^2)=x^2$
$\Rightarrow y^2+2z^2=0$
$\Rightarrow y=0$ and $z=0$
$\therefore$ locus of point is $x-$axis.