Find the point on y-axis which is equidistant from the points (3,… - Vidyadip

Question

Find the point on $y-$axis which is equidistant from the points $(3, 1, 2)$ and $(5, 5, 2).$

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Answer

Let $P(0, y, 0)$ be a point on y-axis which is equidistant from $Q(3, 1, 2)$ and $R(5, 5, 2).$
So
$(PR)^2 = (PQ)^2 \Rightarrow (0 - 5)^2 + (y - 5)^2 + (0 - 2)^2 = (0 - 3) + (y - 1)^2 + (0 + 2)^2$
$\Rightarrow 25 + y^2 + 25 - 10y + 4 = 9 + y^2 + 1 - 2y + 4$
$\Rightarrow -10y + 2y = 14 - 54$
$\Rightarrow -14z - 8z = 16 - 49$
$\Rightarrow -8y = -40$
$\Rightarrow y = 5$
so, the required point is $(0, 5, 0)$

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