Question

The point on y-axis which is at a distance of $\sqrt{10}$ units from the point $(1,2,3)$ is

$\left(a\right)(0,1,0)\left(b\right)(0,2,0)$
$\left(c\right)(0,\sqrt{2},0)\left(d\right)(0,3,0)$

Answer 1

Let $P$ be the point on y-axis.
$\therefore P(0,y,0)$
The point $(1,2,3)$ is at a distance of $\sqrt{10}$ units from $(0,y,0)$.
$\Rightarrow \sqrt{(1-0{)}^2+(2-y{)}^2+(3-0{)}^2}=\sqrt{10}$
Squaring both sides, we get
$\Rightarrow 1+(2-y{)}^2+9=10$
$\Rightarrow (y-2{)}^2=0\Rightarrow y=2$

Hence, the required point is $(0,2,0)$.
Ans : $\left(b\right)$