Find points on the x-axis, each of which is at a distance of 10 units from the point A

Let P (x, 0) be the point on the x-axis. Then as per the question, we have

$A P=10$

$\Rightarrow \sqrt{(x-11)^{2}+(0+8)^{2}}=10$

$\Rightarrow(x-11)^{2}+8^{2}=100$                    (Squaring both sides)

$\Rightarrow(x-11)^{2}=100-64=36$

$\Rightarrow x-11=\pm 6$

$\Rightarrow x=11 \pm 6$

$\Rightarrow x=11-6,11+6$

$\Rightarrow x=5,17$

Hence, the points on the x-axis are (5, 0) and (17, 0).