Find the points on z-axis which are at a distance 21 from the poi… - Vidyadip

Question

Find the points on z-axis which are at a distance $\sqrt{21}$ from the point (1, 2, 3).

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Answer

Let P(0, 0, z) be at a distance of $\sqrt{21}$ from Q(1, 2, 3)
So
$\text{PQ}=\sqrt{(0-1)^2+(0-2)^2+(\text{z}-3)^2}$
$\sqrt{21}=\sqrt{(1)^2+(2)^2+(\text{z}-3)^2}$
$21-5=(\text{z}-3)^2$
$16=(\text{z}-3)^2$
$\text{z}-3=\pm4$
$\text{z}-7\text{ and }\text{z}--1$
So, the required points are (0, 0, 7) and (0, 0, -1)

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