A) \[{{m}_{2}}\]
B) 8
C) 4
D) \[{{m}_{1}}\]
Correct Answer: C
Solution :
Given equation.of parabola is \[{{y}^{2}}-kx+8=0\] \[\Rightarrow \]\[{{y}^{2}}=k\left( x-\frac{8}{k} \right)\]\[\Rightarrow \]\[{{(y-0)}^{2}}=k\left( x-\frac{8}{k} \right)\] The equation of the directrix of this parabola is\[x-\frac{8}{k}=-\frac{k}{4}\] \[[\because x=-a]\] \[\Rightarrow \]\[x=\frac{8}{k}-\frac{k}{4}\] But the equation of the directrix is given as \[x-1=0.\] \[\therefore \]\[\frac{8}{k}-\frac{k}{4}=1\] \[\Rightarrow \]\[{{k}^{2}}+4k-32=0\]\[\Rightarrow \]\[(k-4)(k+8)=0\] \[\therefore \]\[k=-8,4\]
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