The locus of a point whose distance from x-axis is equal to the distance from the
point (1,-1,2) is

Let P(x, y, z )
Distance form X-axis  $=\sqrt{{\mathrm{y}}^2+{\mathrm{z}}^2}$
Distance form P to (1,-1, 2)
$\begin{array}{l}=\sqrt{(\mathrm{x}-1{)}^2+(\mathrm{y}+1{)}^2+(\mathrm{z}-2{)}^2}\\ {\mathrm{y}}^2+{\mathrm{z}}^2={\mathrm{x}}^2+{\mathrm{y}}^2+{\mathrm{z}}^2-2\mathrm{x}+2\mathrm{y}-4\mathrm{z}+6\\ \Rightarrow {\mathrm{x}}^2-2\mathrm{x}+2\mathrm{y}-4\mathrm{z}+6=0\end{array}$