A) \[8\sqrt{2}\]
B) \[16\sqrt{2}\]
C) \[4\sqrt{2}\]
D) \[6\sqrt{2}\]
Correct Answer: A
Solution :
Here we have \[x=8\,\sec \theta ,\,y=8\,\tan \theta \] \[{{x}^{2}}=64{{\sec }^{2}}\theta ,\,{{y}^{2}}=64\,{{\tan }^{2}}\theta \] \[\therefore \] \[{{x}^{2}}-{{y}^{2}}=64\,({{\sec }^{2}}\theta -{{\tan }^{2}}\theta )\] \[{{x}^{2}}-{{y}^{2}}=64\] \[\therefore \] It is a rectangular parabola whose eccentricity is \[\sqrt{2}\]. \[\therefore \] We have distance between directories \[=\frac{2a}{e}\] \[=\frac{2\times 8}{\sqrt{2}}\] \[=8\sqrt{2}\]
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