Question

The points on Y-axis at a distance of 13 units from point (–5, 7) are_______.

$\left[3\right]$

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 $\sqrt{(x_2-x_1{)}^2+(y_2-y_1{)}^2}$

$\left[1\right]$


$\Rightarrow (y-7{)}^2+5^2={13}^2$
$\Rightarrow y^2-14y+49+25=169$
$\Rightarrow y^2-14y-95=0$
$\left[1\right]$

On factorising above equation, we get,
$y^2-19y+5y-95=0$
$\Rightarrow (y-19)(y+5)=0$
$\Rightarrow y=19,-5$

$\therefore$ The points are (0, 19) and (0, -5).
$\left[1\right]$