A) \[y=6/\sqrt{13}\]
B) \[x=6/\sqrt{13}\]
C) \[y=9/\sqrt{13}\]
D) \[x=\pm 9/\sqrt{13}\]
Correct Answer: D
Solution :
Key Idea: If the equation of hyperbola is\[\frac{{{x}^{2}}}{{{a}^{2}}}-\frac{{{y}^{2}}}{{{b}^{2}}}=1\], then equation of directrices are\[x=\pm \frac{a}{e}\]. Given equation of hyperbola be \[\frac{{{x}^{2}}}{9}-\frac{{{y}^{2}}}{4}=1\] Here, \[{{a}^{2}}=9,\,\,{{b}^{2}}=4\] \[\therefore \] \[e=\sqrt{1+\frac{{{b}^{2}}}{{{a}^{2}}}}=\sqrt{1+\frac{4}{9}}\] \[\therefore \]Equation of directrices,\[x=\pm \frac{a}{e}=\pm \frac{9}{\sqrt{13}}\]
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