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,

$\sqrt{(1-0{)}^2+(2-y{)}^2+(3-0{)}^2}=\sqrt{10}$

$\Rightarrow 1+4+-4y+y^2+9=10$

$\Rightarrow y^2-4y+4=0$

$\Rightarrow (y-2{)}^2=0$

$\Rightarrow y=2,2$

$\text{Hence, the required point is}$ (0, 2, 0)