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Question: Answered & Verified by Expert
If the rectangular hyperbola is $x^{2}-y^{2}=64$. Then, which of the following is not correct?
MathematicsHyperbolaJEE Main
Options:
  • A The length of latus rectum is 16
  • B The eccentricity is $\sqrt{2}$
  • C The asymptotes are parallel to each other
  • D The directrices are $x=\pm 4 \sqrt{2}$
Solution:
2352 Upvotes Verified Answer
The correct answer is: The directrices are $x=\pm 4 \sqrt{2}$
Given equation of rectangular hyperbola is $x^{2}-y^{2}=8^{2}$
Length of latusrectum $=2 \times(8)=16$ and eccentricity $=\sqrt{2}$
The asymptotes are perpendicular lines.
So, $x \pm y=0$
Now, directrices are
$x=\pm \frac{8}{\sqrt{2}}=\pm 4 \sqrt{2}$

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