Question

The points on y-axis at a distance of 5 units from point (4, 2) are_______.

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Answer 1

Any point on the y axis is of the form (0, y)
Let, the point be (0, y)

$\because$ The distance between two points $(x_1,y_1)\text{and}(x_2,y_2)$ is $\sqrt{(x_2-x_1{)}^2+(y_2-y_1{)}^2}$

$\left[1\right]$


$\Rightarrow (y-2{)}^2+4^2=5^2$
$\Rightarrow y^2-4y+4+16=25$
$\Rightarrow y^2-4y-5=0$
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On factorising above equation, we get,
$y^2-5y+y-5=0$
$\Rightarrow (y-5)(y+1)=0$
$\Rightarrow y=5,-1$

$\therefore$ The points are (0, 5) and (0, -1).
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