Q67 / 120 · VITEEE 2015 · Mathematics

If the rectangular hyperbola is $x^{2}-y^{2}=64$. Then, which of the following is not correct?

  • A
    The length of latus rectum is 16
  • B
    The eccentricity is $\sqrt{2}$
  • C
    The asymptotes are parallel to each other
  • Correct answer
    D
    The directrices are $x=\pm 4 \sqrt{2}$

Solution

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 $x=\pm \frac{8}{\sqrt{2}}=\pm 4 \sqrt{2}$

Hence, the correct answer is option: 'D'.

Relevant Questions