If the rectangular hyperbola is x² - y² = 64. Then, which of the following is not correct?

Correct Answer is : The asymptotes are parallel to each other

The length of latus rectum is 16

The asymptotes are parallel to each other

The directrices are x = ± 4 {2}

Correct Answer is : The asymptotes are parallel to each other

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VITEEE 2015 Paper

Section: Mathematics

Question : 107 of 120

Marks: +1, -0

x^2 - y^2

= 64. Then, which of the following is not correct?

Solution:

Given equation of rectangular hyperbola is

x^{2}-y^{2}=8^{2}

Here,

a=8

and

b=a

Length of latus rectum

=2 \times \; \frac{b^{2}}{a}=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, statement given in C is not correct.

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