Question

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

Answer 1

The given point is P=( 3,−2,5 ) .

Let the point on the y axis which is at a distance 5 2  units from P be ( 0,y,0 ) .

Distance d between two points ( x 1 , y 1 , z 1 ) and ( x 2 , y 2 , z 2 ) is,

d= ( x 2 − x 1 ) 2 + ( y 2 − y 1 ) 2 + ( z 2 − z 1 ) 2

=

Using the distance formula,

5 2 = ( 0−3 ) 2 + ( y−( −2 ) ) 2 + ( 0−5 ) 2 ( 5 2 ) 2 = ( ( 0−3 ) 2 + ( y−( −2 ) ) 2 + ( 0−5 ) 2 ) 2 50= ( −3 ) 2 + ( y+2 ) 2 + ( −5 ) 2 50=9+ y 2 +4y+4+25 y 2 +4y−12=0

Solving for y ,

y 2 +6y−2y−12=0 y( y+6 )−2( y+6 )=0 ( y+6 )( y−2 )=0 y=2,−6

Thus, the coordinates of points on y-axis which are at a distance of 5 2  units from the given point P( 3,−2,5 ) are ( 0,2,0 ) and ( 0,−6,0 ) .