• # question_answer The line $x-1=0$ is the directrix of the parabola ${{y}^{2}}-kx+8=0$. Then one of the values of k is  [IIT Screening 2000] A)            $\frac{1}{8}$                            B)            8 C)            4      D)            $\frac{1}{4}$

The parabola is ${{y}^{2}}=4.\frac{k}{4}\left( x-\frac{8}{k} \right)$.                   Putting $y=Y,\,x-\frac{8}{k}=X,$ the equation is ${{Y}^{2}}=4.\,\frac{k}{4}.X.$                   \ The directrix  is $X+\frac{k}{4}=0,$i.e. $x-\frac{8}{k}+\frac{k}{4}=0$.                    But $x-1=0$ is the directrix. So, $\frac{8}{k}-\frac{k}{4}=1$ $\Rightarrow \,k=-8,\,4.$