Question

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

• A. $(0,6,0)$ or $(0,-2,0)$
• B. $(0,-6,0)$ or $(0,2,0)$
• C. $(0,4,0)$ or $(0,-4,0)$
• D. $(0,5,0)$ or $(0,-5,0)$

Answer 1

The correct option is B $(0,-6,0)$ or $(0,2,0)$

$sincepointisany-axis$

$itsxandzcoordinateis0$

$Letpt.ony-axisbeA(0,a,0)$

$PA=\sqrt{{(x_2-x_1)}^2+{(y_2-y_1)}^2+{(z_2-z_1)}^2}$

$5\sqrt{2}=\sqrt{{(-3)}^2+{(a+2)}^2+{(0-5)}^2}$

$5\sqrt{2}=\sqrt{a+a^2+4+4a+25}$

$5\sqrt{2}=\sqrt{a^2+4a+38}$

$25\times 2=a^2+4a+38$

$a^2+4a-12=0$

$a^2+6a-2(a+b)=0$

$a=2,a=-6$

$co-ordinateofpoint(0,2,0)and(0,-6,0)$