Find the points on the $\displaystyle x$-axis, each of which is at a distance of $\displaystyle 10$ units from the point A$\displaystyle (11, - 8)$.

Let the point on x-axis be P(x, $\displaystyle 0$) \[\begin{aligned} & P A=10 \Rightarrow P A^{2}=100 \\ & (x-11)^{2}+(0+8)^{2}=100 \\ & (x-11)^{2}=100-64=36 \\ & x-11=6,-6 \\ & x=17,5 \end{aligned} \]