A) \[\frac{1}{8}\]
B) 8
C) 4
D) \[\frac{1}{4}\]
Correct Answer: C
Solution :
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, \[\frac{8}{k}-\frac{k}{4}=1\] \[\Rightarrow \,k=-8,\,4.\]You need to login to perform this action.
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