The line $\frac{x-2}{3}=\frac{y+1}{2}=\frac{z-1}{-1}$ intersects the curve $xy=c^2,z=0,\mathrm{if}c=$

we have z=0 for the point ,where the line intersects the curve ,there fore

$\begin{array}{l}\frac{x-2}{3}=\frac{y+1}{2}=\frac{0-1}{-1}\Rightarrow \frac{x-2}{3}=1and\frac{y+1}{2}=1\\ x=5andy=1c^2=5\Rightarrow c=\pm \sqrt{5}\end{array}$