Find the coordinates of a point on Y-axis which are at a distance of 52 from the point P(3, - 2,5).

Let any point on the Y-axis is A(0 ,y,0).Given, distance between P and A, PA =52⇒ (3−0)2+(−2−y)2+(5−0)2=52On squaring both sides, we get(3−0)2+(−2−y)2+(5−0)2=50⇒9+4+y2+4y+25=50⇒y2+4y+38−50=0⇒y2+4y−12=0⇒(y+6)(y−2)=0⇒y=−6,2Hence, the points on Y-axis are (0 , - 6,0) or (0,2,0).