Find the points on the y-axis, each of which is at a distance of 13 units from the point (-5, 7).

Let A (-5, 7) be the given point, and let P (0, y) be the required point on the y-axis. Then

PA = 13 Units

=> PA² = 169

$\Rightarrow {\left(0+5\right)}^2+{\left(\mathrm{y}-7\right)}^2=169$

$\Rightarrow 25+{\mathrm{y}}^2-14\mathrm{y}+49=169$

$\Rightarrow {\mathrm{y}}^2-14\mathrm{y}+74=169$

$\Rightarrow {\mathrm{y}}^2-14\mathrm{y}-95=0$

$\Rightarrow \left(\mathrm{y}-19\right)\left(\mathrm{y}+5\right)=0$

$\Rightarrow \mathrm{y}-19=0$,or $\Rightarrow \mathrm{y}+5=0$

$\Rightarrow \mathrm{y}=19$ or, $\mathrm{y}=-5$

Hence the required points are (0, 19) and (0, -5).