If the line  x-1=0 is a directrix of the hyperbola ${\mathrm{kx}}^2-{\mathrm{y}}^2=6$ then the hyperbola passes through the point --------- 

$e^2=\frac{{\mathrm{a}}^2+{\mathrm{b}}^2}{{\mathrm{a}}^2}\Rightarrow \mathrm{e}=\sqrt{1+\mathrm{k}}\frac{ }{ }$
also $\mathrm{a}=\sqrt{\frac{6}{\mathrm{k}}}$
Direction is $\mathrm{x}=\frac{\mathrm{a}}{\mathrm{e}}\Rightarrow \mathrm{x}=\sqrt{\frac{6}{\mathrm{k}(\mathrm{k}+1)}}\left(\text{ Directix }\right)$
Now data $\Rightarrow$directix is x=1
Thus $\sqrt{\frac{6}{\mathrm{k}(\mathrm{k}+1)}}=1\Rightarrow \mathrm{k}=2$
$\mathrm{k}=2\to$Hyperbola is $2{\mathrm{x}}^2-{\mathrm{y}}^2=6$ opt (C) satisfies  $2{\mathrm{x}}^2-{\mathrm{y}}^2=6$