Question

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

Answer 1

We know that the x and z coordinates of the point on the y-axis are 0.
So, let the required point be (0, y, 0)
Now,
$$\begin{gathered} \sqrt{{\left(1-0\right)}^2+{\left(2-y\right)}^2+{\left(3-0\right)}^2}=\sqrt{10} \\ \Rightarrow 1+4-4y+y^2+9=10 \\ \Rightarrow y^2-4y+4=0 \\ \Rightarrow {\left(y-2\right)}^2=0 \\ \Rightarrow y=2,2 \end{gathered}$$
Hence, the required point is (0, 2, 0)