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

Solution:

If a point is on the y - axis, then x - coordinate and the z -coordinate of the point are zero.

Let A(0, b, 0) be the point on the y - axis at a distance of 5√2 from point P (3, - 2, 5).

Accordingly, AP = 5√2

On squaring both sides, we obtain AP² = 50

Using the 3d distance formula,

(3 - 0)² + (- 2 - b)² + (5 - 0)² = 50

9 + 4 + b² + 4b + 25 = 50

b² + 4b - 12 = 0

b² + 6b - 2b - 12 = 0

(b + 6)(b - 2) = 0

 b = - 6 and b = 2

Thus, the coordinates of the required point are (0, 2, 0) and (0, - 6, 0)

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NCERT Solutions Class 11 Maths Chapter 12 Exercise ME Question 4

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

Summary:

The coordinates of the points on y-axis which are at a distance of 5√2 from the point P (3, - 2, 5) are (0, 2, 0) and (0, - 6, 0)