Question

The coordinates of a point on $y-$axis which are at a distance of $5\sqrt{2}\text{units}$​ from the point $P(3,-2,5)$ is

• A. $(0,2,0)$ and $(0,-6,0)$
• B. $(0,1,0)$ and $(0,-5,0)$
• C. $(0,0,2)$ and $(0,0,-6)$
• D. $(0,-2,0)$ and $(0,5,0)$

Answer 1

The correct option is A $(0,2,0)$ and $(0,-6,0)$

Let $A(0,b,0)$ be the point on the y-axis at a distance of $5\sqrt{2}$​ from point $P(3,-2,5)$.
given, $AP=5\sqrt{2}$
$\Rightarrow A{P}^2=50$
$\Rightarrow (3-0{)}^2+(-2-b{)}^2+(5-0{)}^2=50$
$\Rightarrow 9+4+b^2+4b+25=50$
$\Rightarrow b^2+4b-12=0$
$\Rightarrow b^2+6b-2b-12=0$
$\Rightarrow (b+6)(b-2)$
$\Rightarrow b=-6,2$
Thus, the coordinates of the required points are $(0,2,0)$ and $(0,-6,0)$