QJEEM22Ma6d03: JEE Main 2022 Mathematics - Class 11 JEEM22Ma6d03 Solution: If the line is a directrix of the hyperbola , then the…

Given hyperbola : ${{{x^2}} \over {6/k}} - {{{y^2}} \over 6} = 1$

Eccentricity $= e = \sqrt {1 + {6 \over {6/k}}} = \sqrt {1 + k}$

Directrices : $x = \, \pm \,{a \over e} \Rightarrow x = \, \pm \,{{\sqrt 6 } \over {\sqrt k \sqrt {k + 1} }}$

As given : ${{\sqrt 6 } \over {\sqrt k \sqrt {k + 1} }} = 1$

$\Rightarrow k = 2$

Here hyperbola is ${{{x^2}} \over 3} - {{{y^2}} \over 6} = 1$

Checking the option gives $\left( {\sqrt 5 , - 2} \right)$ satisfies it.