First slide

Introduction to 3-D Geometry

Question

Find the coordinates of a point on Y-axis which are at a distance of $5 \sqrt{2}$ from the point P(3, - 2,5).

Easy

A

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

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

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

None of these

Solution

Let any point on the Y-axis is A(0 ,y,0).
Given, distance between P and A, PA = $5 \sqrt{2}$
$\Rightarrow \sqrt{(3 - 0)^{2} + (- 2 - y)^{2} + (5 - 0)^{2}} = 5 \sqrt{2}$
On squaring both sides, we get
$\begin{array}{l} (3 - 0)^{2} + (- 2 - y)^{2} + (5 - 0)^{2} = 50 \\ \Rightarrow 9 + 4 + y^{2} + 4 y + 25 = 50 \\ \Rightarrow y^{2} + 4 y + 38 - 50 = 0 \\ \Rightarrow y^{2} + 4 y - 12 = 0 \\ \Rightarrow (y + 6) (y - 2) = 0 \\ \Rightarrow y = - 6, 2 \end{array}$
Hence, the points on Y-axis are (0 , - 6,0) or (0,2,0).

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