Question

Find the points on the y-axis which are at a distance of 3 units from the point (2,3,-1)?

Answer 1

Given : Points on the y-axis   at a distance of 3 units from the point (2,3,-1)

To Find :  Points

Solution:

Points on y axis  = ( 0 , y , 0)

as x and z coordinate will be zero

distance of 3 units from the point (2,3,-1)

=> √(2 - 0)² + ( 3 - y)² + (-1 - 0)²   = 3

Squaring both sides

=> 4 + ( 3 - y)²  + 1 + 9

=>  ( 3 - y)² = 4

=> y²  - 6y + 9 = 4

=>  y²  - 6y + 5 = 0

=> (y - 1)(y - 5) = 0

=> y = 1 , y = 5

Points on y axis  = ( 0 , 1 , 0)  or ( 0 , 5 , 0 )  are at a distance of 3 units from the point (2,3,-1)

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