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

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

  1. A

    (0 ,-6,0) or (0 ,2,0)

  2. B

    (0 ,6,0) or (0 ,-2,0)

  3. C

    (0 ,-6,0) or (1,2,0)

  4. D

    None of these

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    Solution:

    Let any point on the Y-axis is A(0 ,y,0).
    Given, distance between P and A, PA =52

     (30)2+(2y)2+(50)2=52

    On squaring both sides, we get

    (30)2+(2y)2+(50)2=509+4+y2+4y+25=50y2+4y+3850=0y2+4y12=0(y+6)(y2)=0y=6,2

    Hence, the points on Y-axis are (0 , - 6,0) or (0,2,0).

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