Find a point on y-axis which is equidistant form the points (5, -… - Vidyadip

Question

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

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Answer

The point lies on y-axis. Its $x = 0$ Let the required point be $p(0, y)$ and let $A(5, -2)$ and $B(-3, 2)$.$\therefore$
$PA = PB$
$\Rightarrow PA^2 = PB^2$
$\Rightarrow (5 - 0)^2 + (-2 - y)^2 = (-3 - 0)^2 + (2 - y)^2$
(By distance formula)
$\Rightarrow 25 + 4 + y^2 + 4y = 9 + 4 - 4y + y^2$
$\Rightarrow y^2 + 4y + 4y - y^2 = 13 - 29$
$\Rightarrow 8y = -16$
$\Rightarrow\ \text{y}=\frac{-16}{8}=-2$
$\therefore$ The reqquired point will be $(0, -2).$

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